Skip to main content

Full text of "How to Lie with Statistics"

See other formats



Penguin Books 

How to Lie with Statistics 

Darrell Huff was bom in 191 3 in Iowa, and grew up there 
and in California. He received his B.A. ('With Distinction' 
and election to Phi Beta Kappa) and M.A. degrees from the 
State University of Iowa, where he did additional graduate 
work in social psychology, including work in statistics and 
mental testing. He has been associate or managing editor of 
several magazines, such as Look and Better Homes & Gardens, 
but for nearly twenty years he has been a free-lance writer of 
articles and occasional short stories for many magazines, 
among them Harper's, Saturday Evening Post, Esquire and the 
New York Times Magazine. He and his wife, also a writer, 
have lived in Spain, Mallorca, Italy, France, Greece, 
Germany, Denmark and in the United States. 

Much of Darrell Huffs writing has to do with mathematics 
and his book How to Take a Chance has also been published in 
Penguins. In 1963 he was awarded a National School Bell 
Award for his work. 


164 974 



pictures by 
Mel Caiman 


How to 
Lie with 

Darrell Huff 

Penguin Books 



Published by the Penguin Group 

Penguin Books Ltd, 27 Wrights Lane, London W8 5TZ, England 

Penguin Books USA Inc., 375 Hudson Street, New York, New York 10014, USA 

Penguin Books Australia Ltd, Ringwood, Victoria, Australia 

Penguin Books Canada Ltd, 10 Alcorn Avenue, Toronto, Ontario, Canada M4V 3B2 

Penguin Books (NZ) Ltd, 182-190 Wairau Road, Auckland 10, New Zealand 

Penguin Books Ltd, Registered Offices: Harmondsworth, Middlesex, England 

First published by Victor Gollancz 1954 
Published in Pelican Books 1973 
Reprinted in Penguin Books 1991 
10 987654321 

Copyright 1954 by Darrell Huff and Irving Geis 

Adaptation from How to Lie with Statistics by Darrell Huff and Irving Geis 

Pictures in this edition copyright © Mel Caiman, 1973 

All rights reserved 

Printed in England by Clays Ltd, St Ives pic 
Set in Linotype Pilgrim 

Except in the United States of America, this book is sold subject 
to the condition that it shall not, by way of trade or otherwise, be lent, 
re-sold, hired out, or otherwise circulated without the publisher's 
prior consent in any form of binding or cover other than that in 
which it is published and without a similar condition including this 
condition being imposed on the subsequent purchaser 

n t? r'lrc '" } 

To my wite 
with good reason 

There are three kinds of lies: lies, damned lies, and statistics. 

- Disraeli 

Statistical thinking will one day be as necessary for efficient 
citizenship as the ability to read and write. 

- H. G. Wells 

It ain't so much the things we don't know that get us in 
trouble. It's the things we know that ain't so. 

- Artemus Ward 

Round numbers are always false. 

- Samuel Johnson 

I have a great subject [statistics] to write upon, but feel 
keenly my literary incapacity to make it easily intelligible 
without sacrificing accuracy and thoroughness. 

- Sir Francis Galton 


Acknowledgements 8 
Introduction 9 

1 The Sample with the Built-in Bias 13 

2 The Well-Chosen Average 29 

3 The Little Figures That Are Not There 37 

4 Much Ado about Practically Nothing 52 

5 The Gee-Whiz Graph 58 

6 The One-Dimensional Picture 64 

7 The Semi-attached Figure 72 

8 Post Hoc Rides Again 84 

9 How to Statisticulate 94 

10 How to Talk Back to a Statistic no 


The pretty little instances of bumbling and 
chicanery with which this book is peppered have 
been gathered widely and not without assistance. 
Following an appeal of mine through the American 
Statistical Association, a number of professional 
statisticians - who, believe me, deplore the misuse 
of statistics as heartily as anyone alive - sent me 
items from their own collections. These people, 
I guess, will be just as glad to remain nameless 
here. I found valuable specimens in a number 
of books too, primarily these: Business Statistics, 
by Martin A. Brumbaugh and Lester S. Kellogg; 
Gauging Tublic Opinion, by Hadley Cantril; 
Graphic Vresentation, by Willard Cope Brinton; 
Vractical Business Statistics, by Frederick E. 
Croxton and Dudley J. Cowden; Basic Statistics, 
by George Simpson and Fritz Kafka; and 
Elementary Statistical Methods, by Helen M. 


ui M'Eik ( m 


With prospects of an end to the hallowed old British 
measures of inches and feet and pounds, the Gallup poll 
people wondered how well known its metric alternative 
might be. They asked in the usual way, and learned that 
even among men and women who had been to a university 
33 per cent had never heard of the metric system. 

Then a Sunday newspaper conducted a poll of its own - 
and announced that 98 per cent of its readers knew about 
the metric system. This, the newspaper boasted, showed 
'how much more knowledgeable' its readers were than 
people generally. 

How can two polls differ so remarkably? 

Gallup interviewers had chosen, and talked to, a carefully 
selected cross-section of the public. The newspaper had 
naively, and economically, relied upon coupons clipped, 
filled in, and mailed in by readers. 

io How to Lie with Statistics 

It isn't hard to guess that most of those readers who were 
unaware of the metric system had little interest in it or the 
coupon; and they selected themselves out of the poll by not 
bothering to clip and participate. This self-selection pro- 
duced, in statistical terms, a biased or unrepresentative 
sample of just the sort that has led, over the years, to an 
enormous number of misleading conclusions. 

A few winters ago a dozen investigators independently 
reported figures on antihistamine pills. Each showed that a 
considerable percentage of colds cleared up after treatment. 
A great fuss ensued, at least in the advertisements, and a 
medical-product boom was on. It was based on an eternally 
springing hope and also on a curious refusal to look past the 
statistics to a fact that has been known for a long time. As 
Henry G. Felsen, a humorist and no medical authority, 
pointed out quite a while ago, proper treatment will cure a 
cold in seven days, but left to itself a cold will hang on for a 

So it is with much that you read and hear. Averages and 
relationships and trends and graphs are not always what 
they seem. There may be more in them than meets the eye, 
and there may be a good deal less. 

The secret language of statistics, so appealing in a fact- 
minded culture, is employed to sensationalize, inflate, con- 
fuse, and oversimplify. Statistical methods and statistical 
terms are necessary in reporting the mass data of social and 
economic trends, business conditions, 'opinion' polls, the 
census. But without writers who use the words with honesty 
and understanding and readers who know what they mean, 
the result can only be semantic nonsense. 

In popular writing on scientific matters the abused stat- 
istic is almost crowding out the picture of the white- 
jacketed hero labouring overtime without time-and-a-half in 
an ill-lit laboratory. Like the 'little dash of powder, little pot 

Introduction n 

of paint', statistics are making many an important fact 'look 
like what she ain't'. A well-wrapped statistic is better than 
Hitler's 'big lie'; it misleads, yet it cannot be pinned on 

This book is a sort of primer in ways to use statistics to 
deceive. It may seem altogether too much like a manual for 
swindlers. Perhaps I can justify it in the manner of the re- 
tired burglar whose published reminiscences amounted to a 
graduate course in how to pick a lock and muffle a footfall: 
the crooks already know these tricks; honest men must 
learn them in self-defence. 





The Sample 
with the 
Built-in Bias 

If you have a barrel of beans, some red and some white, 
there is only one way to find out precisely how many of 
each colour you have: Count 'em. 

There is an easier way to discover about how many are 
red. Pull out a handful of beans and count just those, assum- 
ing that the proportion will be the same all through the 
barrel. If your sample is large enough and selected properly, 
it will represent the whole well enough for most purposes. 
If, however, it fails in either respect it may be far less accu- 
rate than an intelligent guess and have nothing to re- 
commend it except a spurious air of scientific precision. It 
is sad truth that conclusions from such samples, biased by 
the method of selection, or too small, or both, lie behind 
much of what we read or think we know. 

How a sample develops bias is most easily seen by looking 

14 How to Lie with Statistics 

at an extreme example. Suppose you were to send to a group 
of your fellow-citizens a questionnaire that included this 
query: 'Do you like to answer questionnaires?' Add up the 
returns and you would very probably be able to announce 
that an overwhelming majority - which, for greater con- 
viction, you would specify right down to the last decimal - 
of 'a typical cross-section of the population' asserts affection 
for the things. What has happened, of course, is that most of 
those whose answer would have been No have eliminated 
themselves from your sample by flinging your questionnaire 
into the nearest wastebasket. Even if the flingers constituted 
nine out of ten in your original sample you would be fol- 
lowing a time-hallowed practice in ignoring them when you 
announced your findings. 

Do such samples bias themselves in such a way in real 
life? You bet they do. 

Newspapers and news magazines told us a while back 
that some four million American Catholics had become Pro- 
testants in the last ten years. Source was a poll conducted by 
the Reverend Daniel A. Poling, editor of the inter- 
denominational Christian Herald. Time sums up the story: 

The Herald got its figures by polling a cross section of U.S. 
Protestant ministers, The 2,219 clergymen who replied to its 
questionnaire (out of 25,000 polled) reported that they had re- 
ceived a total of 51,361 former Roman Catholics into their 
churches within the past ten years. Projecting his sample, Poling 
got a nationwide estimate of 4,144,366 Catholic-to-Protestant 
converts in a decade. Writes Episcopalian Will Oursler: 'Even 
when allowances are made for error, the total national figure 
could hardly be less than two or three million and in all prob- 
ability runs closer to five million. 

Although it missed a bet in failing to point out the 
significance of the fact, Time deserves a small bow for let- 
ting us know that more than 90 per cent of the ministers 

The Sample with the Built-in Bias 15 

polled did not reply. To destroy this survey completely, we 
have only to note the reasonable possibility that most of the 
90 per cent threw away the questionnaire because they had 
no conversions to report. 

Employing this assumption and using the same figure - 
181,000 - as Dr Poling did for the total number of Protestant 
ministers with pastoral charges, we can make our own pro- 
jection. Since he went to 25,000 out of 181,000 and found 
51,361 conversions, asking everybody should have produced 
a conversion total of 370,000 or so. 

Our crude methods have produced a very dubious figure, 
but it is at least as worthy of trust as the one that was 
published nationally - one that is eleven times as big as 
ours and therefore far more exciting. 

As for Mr O's confident 'allowances . . . for error', well, if 
he has discovered a method to compensate for errors of un- 
known magnitude, the world of statistics will be grateful. 

With this background, let us work over a news report - 
from some years back when it represented even more 
money than it does now - that 'the average Yale man, Class 
of '24, makes $25,111 a year'. 

Well, good for him! 

But wait a minute. What does this impressive figure 
mean? Is it, as it appears to be, evidence that if you send 
your boy to Yale, or, for all I know, Oxbridge, you won't 
have to work in your old age and neither will he? 

Two things about the figure stand out at first suspicious 
glance. It is surprisingly precise. It is quite improbably salu- 

There is small likelihood that the average income of any 
far-flung group is ever going to be known down to the 
dollar. It is not particularly probable that you know your 
own income for last year so precisely as that unless it was all 
derived from salary. And $25,000 incomes are not often 

16 How to Lie with Statistics 

all salary; people in that bracket are likely to have well- 
scattered investments. 

Furthermore, this lovely average is undoubtedly cal- 
culated from the amounts the Yale men said they earned. 
Even if they had the honour system in New Haven in '24, we 
cannot be sure that it works so well after a quarter of a 
century that all these reports are honest ones. Some people 
when asked their incomes exaggerate out of vanity or op- 

timism. Others minimize, especially, it is to be feared, on 
income-tax returns; and having done this may hesitate to 
contradict themselves on any other paper. Who knows what 
the revenuers may see? It is possible that these two ten- 
dencies, to boast and to understate, cancel each other out, 
but it is unlikely. One tendency may be far stronger than the 
other, and we do not know which one. 

We have begun then to account for a figure that common 
sense tells us can hardly represent the truth. Now let us put 

The Sample with the Built-in Bias 17 

our finger on the likely source of the biggest error, a source 
that can produce $25,111 as the 'average income' of some 
men whose actual average may well be nearer half that 

The report on the Yale men comes from a sample. We can 
be pretty sure of that because reason tells us that no one can 
get hold of all the living members of that class of '24. There 
are bound to be many whose addresses are unknown 
twenty-five years later. 

And, of those whose addresses are known, many will not 
reply to a questionnaire, particularly a rather personal one. 
With some kinds of mail questionnaire, a five or ten per cent 
response is quite high. This one should have done better than 
that, but nothing like one hundred per cent. 

So we find that the income figure is based on a sample 
composed of all class members whose addresses are known 
and who replied to the questionnaire. Is this a representative 
sample? That is, can this group be assumed to be equal in 
income to the unrepresented group, those who cannot be 
reached or who do not reply? 

Who are the little lost sheep down in the Yale rolls as 
'address unknown'? Are they the big-income earners - the 
Wall Street men, the corporation directors, the manu- 
facturing and utility executives? No; the addresses of the 
rich will not be hard to come by. Many of the most prosper- 
ous members of the class can be found through Who's Who 
in America and other reference volumes even if they have 
neglected to keep in touch with the alumni office. It is a 
good guess that the lost names are those of the men who, 
twenty-five years or so after becoming Yale bachelors of 
arts, have not fulfilled any shining promise. They are clerks, 
mechanics, tramps, unemployed alcoholics, barely surviving 
writers and artists . . . people of whom it would take half a 
dozen or more to add up to an income of $25,1 1 1. These men 

18 How to Lie with Statistics 

do not so often register at class reunions, if only because 
they cannot afford the trip. 

Who are those who chucked the questionnaire into the 
nearest wastebasket? We cannot be so sure about these, but 
it is at least a fair guess that many of them are just not 
making enough money to brag about. They are a little like 
the fellow who found a note clipped to his first pay cheque 
suggesting that he consider the amount of his salary 
confidential and not material for the interchange of office 
confidences. 'Don't worry,' he told the boss. 'I'm just as 
ashamed of it as you are.' 

It becomes pretty clear that the sample has omitted two 
groups most likely to depress the average. The $25,1 1 1 figure 
is beginning to explain itself. If it is a true figure for any- 
thing it is one merely for that special group of the class of 
'24 whose addresses are known and who are willing to stand 
up and tell how much they earn. Even that requires an as- 
sumption that the gentlemen are telling the truth. 

Such an assumption is not to be made lightly. Experience 
from one breed of sampling study, that called market re- 
search, suggests that it can hardly ever be made at all. A 
house-to-house survey purporting to study magazine read- 
ership was once made in which a key question was: What 
magazine does your household read? When the results were 
tabulated and analysed it appeared that a great many people 
loved Harper's, which if not highbrow is at least upper 
middlebrow, and not very many read True Story, which is 
very lowbrow indeed. Yet there were publishers' figures 
around at the time that showed very clearly that True Story 
had more millions of circulation than Harper's had hundreds 
of thousands. Perhaps we asked the wrong kind of people, 
the designers of the survey said to themselves. But no, the 
questions had been asked in all sorts of neighbourhoods all 
around the country. The only reasonable conclusion then 

The Sample with the Built-in Bids 1 9 

was that a good many of the respondents, as people are 
called when they answer such questions, had not told the 
truth. About all the survey had uncovered was snobbery. 

In the end it was found that if you wanted to know what 
certain people read it was no use asking them. You could 
learn a good deal more by going to their houses and saying 
you wanted to buy old magazines and what could be had? 

Then all you had to do was count the Yale Reviews and the 
Love Romances. Even that dubious device, of course, does 
not tell you what people read, only what they have been 
exposed to. 

Similarly, the next time you learn from your reading that 
the average man (you hear a good deal about him these days, 
most of it faintly improbable) brushes his teeth 1-02 times a 
day - a figure I have just made up, but it may be as good as 
anyone else's - ask yourself a question. How can anyone 
have found out such a thing? Is a woman who has read 
in countless advertisements that non-brushers are social 

20 How to Lie with Statistics 

offenders going to confess to a stranger that she does not 
brush her teeth regularly? The statistic may have meaning to 
one who wants to know only what people say about tooth- 
brushing but it does not tell a great deal about the frequency 
with which bristle is applied to incisor. 

A river cannot, we are told, rise above its source. Well, it 
can seem to if there is a pumping station concealed some- 
where about. It is equally true that the result of a sampling 
study is no better than the sample it is based on. By the time 
the data have been filtered through layers of statistical man- 
ipulation and reduced to a decimal-pointed average, the 
result begins to take on an aura of conviction that a closer 
look at the sampling would deny. 

To be worth much, a report based on sampling must use a 
representative sample, which is one from which every 
source of bias has been removed. That is where our Yale 
figure shows its worthlessness. It is also where a great many 
of the things you can read in newspapers and magazines 
reveal their inherent lack of meaning. 

A psychiatrist reported once that practically everybody is 
neurotic. Aside from the fact that such use destroys any 
meaning in the word 'neurotic', take a look at the man's 
sample. That is, whom has the psychiatrist been observing? 
It turns out that he has reached this edifying conclusion 
from studying his patients, who are a long, long way from 
being a sample of the population. If a man were normal, our 
psychiatrist would never meet him. 

Give that kind of second look to the things you read, and 
you can avoid learning a whole lot of things that are not 

It is worth keeping in mind also that the dependability of 
a sample can be destroyed just as easily by invisible sources 
of bias as by these visible ones. That is, even if you can't find 
a source of demonstrable bias, allow yourself some degree of 

The Sample with the Built-in Bias 2 1 

scepticism about the result as long as there is a possibility of 
bias somewhere. There always is. The American presidential 
elections in 1948 and 1952 were enough to prove that, if 
there were any doubt. 

For further evidence go back to 1936 and the Literary 
Digest's famed fiasco. The ten million telephone and Digest 





subscribers who assured the editors of the doomed magazine 
that it would be Landon 370, Roosevelt 161 came from the 
list that had accurately predicted the 1932 election. How 
could there be bias in a list already so tested? There was a 
bias, of course, as college theses and other post mortems 
found: People who could afford telephones and magazine 
subscriptions in 1936 were not a cross section of voters. 
Economically they were a special kind of people, a sample 
biased because it was loaded with what turned out to 

22 How to Lie with Statistics 

be Republican voters. The sample elected Landon, but the 
voters thought otherwise. 

The basic sample is the kind called 'random*. It is selected 
by pure chance from the 'universe', a word by which the 
statistician means the whole of which the sample is a part. 
Every tenth name is pulled from a file of index cards. Fifty 
slips of paper are taken from a hatful. Every twentieth 
person met in Piccadilly is interviewed. (But remember that 
this last is not a sample of the population of the world, or of 
England, or of San Francisco, but only of the people in Pic- 
cadilly at the time. One interviewer for an opinion poll said 
that she got her people in a railroad station because 'all 
kinds of people can be found in a station'. It had to be 
pointed out to her that mothers of small children, for in- 
stance, might be under-represented there.) 

The test of the random sample is this: Does every name or 
thing in the whole group have an equal chance to be in the 

The purely random sample is the only kind that can be 
examined with entire confidence by means of statistical 
theory, but there is one thing wrong with it. It is so difficult 
and expensive to obtain for many uses that sheer cost elimi- 
nates it. A more economical substitute, which is almost uni- 
versally used in such fields as opinion polling and market 
research, is called stratified random sampling. 

To get this stratified sample you divide your universe into 
several groups in proportion to their known prevalence. And 
right there your trouble can begin: Your information about 
their proportion may not be correct. You instruct your 
interviewers to see to it that they talk to so many Negroes 
and such-and-such a percentage of people in each of several 
income brackets, to a specified number of farmers, and so 
on. All the while the group must be divided equally between 
persons over forty and under forty years of age. 

The Sample with the Built-in Bias 23 

That sounds fine - but what happens? On the question of 
Negro or white the interviewer will judge correctly most of 
the time. On income he will make more mistakes. As to 
farmers - how do you classify a man who farms part time 
and works in the city too? Even the question of age can pose 
some problems which are most easily settled by choosing 
only respondents who obviously are well under or well over 
forty. In that case the sample will be biased by the virtual 
absence of the late-thirties and early-forties age groups. You 
can't win. 

I skevrfct he tmci k*tf**s- 

On top of all this, how do you get a random sample 
within the stratification? The obvious thing is to start with a 
list of everybody and go after names chosen from it at 
random; but that is too expensive. So you go into the streets 
- and bias your sample against stay-at-homes. You go from 
door to door by day - and miss most of the employed 
people. You switch to evening interviews - and neglect the 
movie-goers and night-clubbers. 

24 How to Lie with Statistics 

The operation of a poll comes down in the end to a run- 
ning battle against sources of bias, and this battle is con- 
ducted all the time by all the reputable polling 
organizations. What the reader of the reports must remem- 
ber is that the battle is never won. No conclusion that 'sixty- 
seven per cent of the British people are against' something or 
other should be read without the lingering question. Sixty- 
seven per cent of which British people? 



So with the late Dr Alfred C. Kinsey's 'male volume' and 
'female volume'. Splendid ground-breakers though they have 
proved to be, they are cursed by sampling that is distress- 
ingly far from random. It is bad enough that the samples list 
heavily in such peculiar -directions as college educated 
(seventy-five per cent of the women) and prison residence. A 

The Sample with the Built-in Bias 2£ 

more serious weakness because harder to allow for is the 
probability that the samples lean sharply towards sexual 
exhibitionists; for folks who volunteer to tell all when the 
subject is sex may well differ sharply in their sexual his- 
tories from the more taciturn who have weeded themselves 
out of the samples by saying the hopeful interviewers 

That all this is more than speculation is confirmed by a 
study made by A. H. Maslow at Brooklyn College. Among 
girl students in his sample were many who later volunteered 
for kinseying, and Maslow found that these girls were gen- 
erally the more sexually unconventional and sexually soph- 
isticated ones. 

The problem when reading Kinsey, or any of the more 
recent studies of sexual behaviour for that matter, is how to 
study it without learning too much that is not necessarily so. 
The danger is acute with any research based on sampling, 
and it is likely to become even more so when you take your 
big book or major research report in the form of a popular 

For one thing, there are at least three levels of sampling 
involved in work like Kinsey's. As already noted, the 
samples of the population (first level) are far from random 
and so may not be particularly representative of any popu- 
lation. It is equally important to remember that any ques- 
tionnaire is only a sample (another level) of the possible 
questions; and that the answer the gentleman or lady gives is 
no more than a sample (third level) of his or her attitudes 
and experiences on each question. 

It may be true with the Kinsey kind of work, as it has 
been found to be elsewhere, that the kind of people who 
make up an interviewing staff can shade the results in an 
interesting fashion. Several skirmishes back, sometime 
during World War Two, the National Opinion Research 

26 How to Lie with Statistics 

Center sent out two staffs of interviewers to ask three ques- 
tions of five hundred Negroes in a Southern city of the 
United States. White interviewers made up one staff, black 
the other. 

One question was, 'Would Negroes be treated better or 
worse here if the Japanese conquered the U.S.A.?' Negro 
interviewers reported that nine per cent of those they asked 
said 'better'. White interviewers found only two per cent of 
such responses. And while Negro interviewers found only 
twenty-five per cent who thought Negroes would be treated 
worse, white interviewers turned up forty-five per cent. 

When 'Nazis' was substituted for 'Japanese' in the ques- 
tion, the results were similar. 

The third question probed attitudes that might be based on 
feelings revealed by the first two. 'Do you think it is more 
important to concentrate on beating the Axis, or to make 
democracy work better here at home?' 'Beat the Axis' was 
the reply of thirty-nine per cent, according to the Negro 

The Sample with the Built-in Bias 27 

interviewers; of sixty-two per cent, according to the 

Here is bias introduced by unknown factors. It seems 
likely that the most effective factor was a tendency that 
must always be allowed for in reading polls results, a desire 
to give a pleasing answer. Would it be any wonder if, when 
answering a question with connotations of disloyalty in 
wartime, a Southern Negro would tell a white man what 
sounded good rather than what he actually believed? It is 
also possible that the different groups of interviewers chose 
different kinds of people to talk to. 

In any case the results are obviously so biased as 
worthless. You can judge for yourself how many other poll- 
based conclusions are just as biased, just as worthless - but 
with no check available to show them up. 

You have pretty fair evidence to go on if you suspect that 
polls in general are biased in one specific direction, the direc- 
tion of the Literary Digest error. This bias is towards the 
person with more money, more education, more infor- 
mation and alertness, better appearance, more conventional 
behaviour, and more settled habits than the average of the 
population he is chosen to represent. 

You can easily see what produces this. Let us say that you 
are an interviewer assigned to a street corner, with one inter- 
view to get. You spot two men who seem to fit the category 
you must complete: over forty, Negro, urban. One is in clean 
overalls, decently patched, neat. The other is dirty and he 
looks surly. With a job to get done, you approach the more 
likely-looking fellow, and your colleagues all over the 
country are making similar decisions. 

Some of the strongest feeling against public-opinion polls 
is found in liberal or left-wing circles, where it is rather 
commonly believed that polls are generally rigged. Behind 
this view is the fact that poll results so often fail to square 

28 How to Lie with Statistics 

with the opinions and desires of those whose thinking is not 
in the conservative direction. Polls, they point out, seem to 
elect Republicans even when voters shortly thereafter do 

Actually, as we have seen, it is not necessary that a poll be 
rigged - that is, that the results be deliberately twisted in 
order to create a false impression. The tendency of the 
sample to be biased in this consistent direction can rig it 








You, I trust, are not a snob, and I certainly am not an estate 
agent. But let's say that you are and that I am and that you 
are looking for property to buy along a road I know well. 
Having sized you up, I take pains to tell you that the average 
income in this neighbourhood is some £10,000 a year. 
Maybe that clinches your interest in living here; anyway, 
you buy and that handsome figure sticks in your mind. More 
than likely, since we have agreed that for the purposes of 
the moment you are a bit of a snob, you toss it in casually 
when telling your friends about where you live. 

A year or so later we meet again. As a member of some 
rate-payers' committee I am circulating a petition to keep 
the rates down or assessments down or bus fare down. My 
plea is that we cannot afford the increase: After all, the aver- 
age income in this neighbourhood is only £2,000 a year. 

jo How to Lie with Statistics f\ 


Perhaps you go along with me and my committee in this - c 
you're not only a snob, you're stingy too - but you can't [ 
help being surprised to hear about that measly £2,000. Am I •' 
lying now, or was I lying last year? 

You can't pin it on me either time. That is the essential f 
beauty of doing your lying with statistics. Both those figures £j 
are legitimate averages, legally arrived at. Both represent the 
same data, the same people, the same incomes. All the same 
it is obvious that at least one of them must be so misleading 
as to rival an out-and-out lie. 

My trick was to use a different kind of average each time, 
the word 'average' having a very loose meaning. It is a trick 
commonly used, sometimes in innocence but often in guilt, 
by fellows wishing to influence public opinion or sell adver- 
tising space. When you are told that something is an average 
you still don't know very much about it unless you can 
find out which of the common kinds of average it is - mean, 
median, or mode. 

The £10,000 figure I used when I wanted a big one is a 
mean, the arithmetic average of the incomes of all the fami- 
lies in the neighbourhood. You get it by adding up all the 
incomes and dividing by the number there are. The smaller 
figure is a median, and so it tells you that half the families in 
question have more than £2,000 a year and half have less. I 
might also have used the mode, which is the most frequently 
met-with figure in a series. If in this neighbourhood there are 
more families with incomes of £3,000 a year than with any 
other amount, £3,000 a year is the modal income. 

In this case, as usually is true with income figures, an 
unqualified 'average' is virtually meaningless. One factor 
that adds to the confusion is that with some kinds of infor- 
mation all the averages fall so close together that, for casual 
purposes, it may not be vital to distinguish among them. 

If you read that the average height of the men of some 

The Well-Chosen Average 31 

primitive tribe is only five feet, you get a fairly good idea of 
the stature of these people. You don't have to ask whether 
that average is a mean, median, or mode; it would come out 
about the same. (Of course, if you are in the business of 
manufacturing overalls for Africans you would want more 
information than can be found in any average. This has to 
do with ranges and deviations, and we'll tackle that one in 
the next chapter.) 

The different averages come out close together when you 
deal with data, such as those having to do with many human 
characteristics, that have the grace to fall close to what is 
called the normal distribution. If you draw a curve to rep- 
resent it you get something shaped like a bell, and mean, 
median, and mode fall at the same point. 

Consequently one kind of average is as good as another 
for describing the heights of men, but for decribing their 
pocketbooks it is not. If you should list the annual incomes 
of all the families in a given city you might find that they 
ranged from not much to perhaps £20,000 or so, and you 
might find a few very large ones. More than nine-five per 
cent of the incomes would be under £5,000, putting them 
way over towards the left-hand side of the curve. Instead of 
being symmetrical, like a bell, it would be skewed. Its shape 
would be a little like that of a child's slide, the ladder rising 
sharply to a peak, the working part sloping gradually down. 
The mean would be quite a distance from the median. You 
can see what this would do to the validity of any com- 
parison made between the 'average' (mean) of one year and 
the 'average' (median) of another. 

In the neighbourhood where I sold you some property the 
two averages are particularly far apart because the dis- 
tribution is markedly skewed. It happens that most of your 
neighbours are small farmers or wage earners employed in a 
near-by village or elderly retired people on pensions. But 

32 How to Lie with Statistics 

three of the inhabitants are millionaire week-enders and 
these three boost the total income, and therefore the arith- 
metical average, enormously. They boost it to a figure that 
practically everybody in the neighbourhood has a good deal 
less than. You have in reality the case that sounds like a 
joke or a figure of speech: Nearly everybody is below 

That's why when you read an announcement by a cor- 
poration executive or a business proprietor that the average 
pay of the people who work in his establishment is so much, 
the figure may mean something and it may not. If the aver- 
age is a median, you can learn something significant from it: 
Half the employees make more than that; half make less. But 
if it is a mean (and believe me it may be that if its nature is 
unspecified) you may be getting nothing more revealing than 
the average of one £25,000 income - the proprietor's - and 
the salaries of a crew of underpaid workers. 'Average annual 
pay of £3,800' may conceal both the £1,400 salaries and 
the owner's profits taken in the form of a whopping 

How neatly this can be worked into a whipsaw device, in 
which the worse the story, the better it looks, is illustrated 
in some company statements. Let's try our hand at one in a 
small way. 

You are one of the three partners who own a small manu- 
facturing business. It is now the end of a very good year. 
You have paid out £99,000 to the ninety employees who do 
the work of making and shipping the chairs or whatever it is 
that you manufacture. You and your partners have paid 
yourselves £5,500 each in salaries. You find there are profits 
for the year of £21,000 to be divided equally among you. 
How are you going to describe this? To make it easy to 
understand, you put it in the form of averages. Since all the 
employees are doing about the same kind of work for 








i3,472 Arithmetical average 






£2,100 Median (the one In the middle.12 above him, 12 below) 


Ei.400 Mode (occurs most frequently) 

34 How to Lie with Statistics 

similar pay it won't make much difference whether you use 
a mean or a median. This is what you come out with: 

Average wageofemployees £1,100 

Average salary and profit of owners 12,500 

That looks terrible, doesn't it? Let's try it another way. Take 
£15,000 of the profits and distribute it among the three part- 
ners as bonuses. And this time when you average up the 
wages, include yourself and your partners. And be sure to 
use a mean. 

Average wage or salary £1,403 

Average profit of owners 2,000 

Ah. That looks better. Not as good as you could make it 
look, but good enough. Less than six per cent of the money 
available for wages and profits has gone into profits, and you 
can go further and show that too if you like. Anyway, 
you've got figures now that you can publish, post on a bul- 
letin board, or use in bargaining. 

This is pretty crude because the example is simplified, but 
it is nothing to what has been done in the name of account- 
ing. Given a complex corporation with hierarchies of em- 
ployees ranging all the way from beginning typist to 
president with a several-hundred-thousand-dollar bonus, all 
sorts of things can be covered up in this manner. 

So when you see an average-pay figure, first ask: Average 
of what? Who's included? The United States Steel Cor- 
poration once said that its employees' average weekly 
earnings went up 107 per cent in less than a decade. So they 
did - but some of the punch goes out of the magnificent in- 
crease when you note the earlier figure includes a much 
larger number of partially employed people. If you work 
half-time one year and full-time the next, your earnings will 

The Well-Chosen Average 35 

double, but that doesn't indicate anything at all about your 
wage rate. 

You may have read in the paper that the income of the 
average American family was $6,940 in some specified year. 
You should not try to make too much out of that figure 
unless you also know what 'family' has been used to mean, 
as well as what kind of average this is. (And who says so and 
how he knows and how accurate the figure is.) 

The figure you saw may have come from the Bureau of 
the Census. If you have the Bureau's full report you'll have 
no trouble finding right there the rest of the information you 
need: that this average is a median; that 'family' signifies 
'two or more persons related to each other and living 
together'. You will also learn, if you turn back to the tables, 
that the figure is based on a sample of such size that there 
are nineteen chances out of twenty that the estimate is cor- 
rect within a margin of, say, $71 plus or minus. 

That probability and that margin add up to a pretty good 
estimate. The Census people have both skill enough and 
money enough to bring their sampling studies down to a fair 
degree of precision. Presumably they have no particular 
axes to grind. Not all the figures you see are born under such 
happy circumstances, nor are all of them accompanied by 
any information at all to show how precise or imprecise 
they may be. We'll work that one over in the next chap- 

Meanwhile you may want to try your scepticism on some 
items from 'A Letter from the Publisher' in Time magazine. 
Of new subscribers it said, Their median age is 34 years and 
their average family income is $7,270 a year.' An earlier 
survey of 'old TiMErs' had found that their 'median age was 
41 years . . . Average income was $9,535 . . .' The natural 
question is why, when median is given for ages both times, 
the kind of average for incomes is carefully unspecified. 

36 How to Lie with Statistics 

Could it be that the mean was used instead because it is 
bigger, thus seeming to dangle a richer readership before 

You might also try a game of what-kind-of-average-are- 
you on the alleged prosperity of the 1924 Yales reported at 
the beginning of Chapter 1. 


n <& tvt uJtTXi®"^** 



The Little 
Figures That 
Are Not There 

What you should do when told the results of a survey, a 
statistician once advised, is ask, 'How many juries did you 
poll before you found this one?' 

As noted previously, well-biased samples can be employed 
to produce almost any result anyone may wish. So can 
properly random ones, if they are small enough and you 
try enough of them. 

Users report 23 percent fewer cavities with Doakes' tooth- 
paste, the big type says. You could do with twenty-three per 
cent fewer aches so you read on. These results, you find, 
come from a reassuringly 'independent' laboratory, and the 
account is certified by a chartered accountant. What more 
do you want? 

Yet if you are not outstandingly gullible or optimistic, 
you will recall from experience that one toothpaste is 

38 How to Lie with Statistics 

seldom much better than any other. Then how can the 
Doakes people report such results? Can they get away with 
telling lies, and in such big type at that? No, and they don't 
have to. There are easier ways and more effective ones. 

The principal joker in this one is the inadequate sample - 
statistically inadequate, that is; for Doakes' purpose it is just 
right. That test group of users, you discover by reading the 
small type, consisted of just a dozen persons. (You have to 
hand it to Doakes, at that, for giving you a sporting chance. 

Some advertisers would omit this information and leave 
even the statistically sophisticated only a guess as to what 
species of chicanery was afoot. His sample of a dozen isn't 
so bad either, as these things go. Something called Dr Cor- 
nish's Tooth Powder came onto the market a few years ago 
with a claim to have shown 'considerable success in cor- 
rection of . . . dental caries'. The idea was that the powder 
contained urea, which laboratory work was supposed to 
have demonstrated to be valuable for the purpose. The 
pointlessness of this was that the experimental work had 
been purely preliminary and had been done on precisely six 

The Little Figures That Are Not There 39 

But let's get back to how easy it is for Doakes to get a 
headline without a falsehood in it and everything certified at 
that. Let any small group of persons keep count of cavities 
for six months, then switch to Doakes'. One of three things 
is bound to happen: distinctly more cavities, distinctly 
fewer, or about the same number. If the first or last of these 

possibilities occurs, Doakes & Company files the figures 
(well out of sight somewhere) and tries again. Sooner or 
later, by the operation of chance, a test group is going to 
show a big improvement worthy of a headline and perhaps 
a whole advertising campaign. This will happen whether 
they adopt Doakes' or baking soda or just keep on using 
their same old dentifrice. 

The importance of using a small group is this: With a 
large group any difference produced by chance is likely to 

40 How to Lie with Statistics 

be a small one and unworthy of big type. A two-per<ent- 
improvement claim is not going to sell much toothpaste. 

How results that are not indicative of anything can be 
produced by pure chance - given a small enough number of 
cases - is something you can test for yourself at small cost. 
Just start tossing a penny. How often will it come up heads? 
Half the time, of course. Everyone knows that. 

Well, let's check that and see ... I have just tried ten 
tosses and got heads eight times, which proves that pennies 
come up heads eighty per cent of the time. Well, by tooth- 
paste statistics they do. Now try it yourself. You may get a 
fifty-fifty result, but probably you won't; your result, like 
mine, stands a good chance of being quite a way away from 
fifty-fifty. But if your patience holds out for a thousand 
tosses you are almost (though not quite) certain to come out 
with a result very close to half heads - a result, that is, 

The Little Figures That Are Not There 41 

which represents the real probability. Only when there is a 
substantial number of trials involved is the law of averages a 
useful description or prediction. 

How many is enough? That's a tricky one too. It depends 
among other things on how large and how varied a popu- 
lation you are studying by sampling. And sometimes the 
number in the sample is not what it appears to be. 

A remarkable instance of this came out in connection 
with a test of a polio vaccine some years ago. It appeared to 
be an impressively large-scale experiment as medical ones 
go: 450 children were vaccinated in a community and 680 
were left unvaccinated, as controls. Shortly thereafter the 
community was visited by an epidemic. Not one of the vac- 
cinated children contracted a recognizable case of polio. 

Neither did any of the controls. What the experimenters 
had overlooked or not understood in setting up their project 
was the low incidence of paralytic polio. At the usual rate, 
only two cases would have been expected in a group of this 
size, and so the test was doomed from the start to have no 
meaning. Something like fifteen to twenty-five times this 
many children would have been needed to obtain an answer 
signifying anything. 

Many a great, if fleeting, medical discovery has been 
launched similarly. 'Make haste', as one physician* put it, 
'to use a new remedy before it is too late.' 

The guilt does not always lie with the medical profession 
alone. Public pressure and hasty journalism often launch a 
treatment that is unproved, particularly when the demand is 
great and the statistical background hazy. So it was with the 
cold vaccines that were popular some years back and the 

* These words have been attributed to both Sir William Osier and 
Edward Livingston Trudeau. Choose one. Since they were both 
physicians and pretty sharp on our subject, it is quite possible that 
they both said it, give or take a word or two. 

42 How to Lie with Statistics 

antihistamines more recently. A good deal of the popularity 
of these unsuccessful 'cures' sprang from the unreliable 
nature of the ailment and from a defect of logic. Given time, 
a cold will cure itself. 

How can you avoid being fooled by inconclusive results? 
Must every man be his own statistician and study the raw 
data for himself? It is not that bad; there is a test of 
significance that is easy to understand. It is simply a way of 
reporting how likely it is that a test figure represents a real 
result rather than something produced by chance. This is the 
little figure that is not there - on the assumption that you, 
the lay reader, wouldn't understand it. Or that, where 
there's an axe to grind, you would. 

If the source of your information gives you also the 
degree of significance, you'll have a better idea of where you 
stand. This degree of significance is most simply expressed as 
a probability, as when the Bureau of the Census tells you 
that there are nineteen chances out of twenty that their 
figures have a specified degree of precision. For most pur- 
poses nothing poorer than this five per cent level of 
significance is good enough. For some the demanded level is 
one per cent, which means that there are ninety-nine 
chances out of a hundred that an apparent difference, or 
whatnot, is real. Anything this likely is sometimes described 
as 'practically certain'. 

There's another kind of little figure that is not there, one 
whose absence can be just as damaging. It is the one that 
tells the range of things or their deviation from the average 
that is given. Often an average - whether mean or median, 
specified or unspecified - is such an oversimplification that it 
is worse than useless. Knowing nothing about a subject is 
frequently healthier than knowing what is not so, and a 
little learning may be a dangerous thing. 

Altogether too much housing, for instance, has been 

The Little Figures That Are Not There 43 

planned to fit the statistically average family of 3-6 persons. 
Translated into reality this means three or four persons, 
which, in turns, means two bedrooms. And this size family, 
'average' though it is, actually makes up a minority of all 
families. 'We build average houses for average families,' say 
the builders - and neglect the majority that are larger or 
smaller. Some areas, in consequence of this, have been over- 


built with two-bedroom houses, underbuilt in respect to 
smaller and larger units. So here is a statistic whose mis- 
leading incompleteness has had costly consequences. Of it a 
large public-health group has said: 'When we look beyond 
the arithmetical average to the actual range which it mis- 
represents, we find that the three-person and four-person 
families make up only 45 per cent of the total. Thirty-five 
per cent are one-person and two-person; 20 per cent have 
more than four persons.' 

44 How to Lie with Statistics 

Common sense has somehow failed in the face of the 
convincingly precise and authoritative 3-6. It has some- 
how outweighed what everybody knows from observa- 
tion: that many families are small and quite a few are 

In somewhat the same fashion those little figures that are 
missing from what are called 'Gesell's norms' have produced 
pain in papas and mamas. Let a parent read, as many have 
done in such places as Sunday papers, that 'a child' learns to 
sit erect at the age of so many months and he thinks at once 
of his own child. Let his child fail to sit by the specified age 
and the parent must conclude that his offspring is 'retarded' 
or 'subnormal' or something equally invidious. Since half the 
children are bound to fail to sit by the time mentioned, a 
good many parents are made unhappy. Of course, speaking 
mathematically, this unhappiness is balanced by the joy of 
the other fifty per cent of parents in discovering that their 
children are 'advanced'. But harm can come of the efforts of 
the unhappy parents to force their children to conform to 
the norms and thus be backward no longer. 

All this does not reflect on Dr Arnold Gesell or his 
methods. The fault is in the filtering-down process from the 
researcher through the sensational or ill-informed writer to 
the reader who fails to miss the figures that have disap- 
peared in the process. A good deal of the misunderstanding 
can be avoided if to the 'norm' or average is added an indi- 
cation of the range. Parents seeing that their youngsters fall 
within the normal range will quit worrying about small and 
meaningless differences. Hardly anybody is exactly normal 
in any way, just as one hundred tossed pennies will rarely 
come up exactly fifty heads and fifty tails. 

Confusing 'normal' with 'desirable' makes it all the worse. 
Dr Gesell simply stated some observed facts; it was the 
parents who, in reading the books and articles, concluded 

The Little Figures That Are Not There 45 

that a child who walks late by a day or a month must be 

A good deal of the sillier criticism of Dr Alfred Kinsey"s 
well-known (if hardly well-read) report came from taking 
normal to be equivalent to good, right, desirable. Dr Kinsey 
was accused of corrupting youth by giving them ideas and 
particularly by calling all sorts of popular but unapproved 
sexual practices normal. But he simply said that he had 
found these activities to be usual, which is what normal 
means, and he did not stamp them with any seal of ap- 
proval. Whether they were naughty or not did not come 
within what Dr Kinsey considered to be his province. So he 
ran up against something that has plagued many another 
observer: It is dangerous to mention any subject having high 
emotional content without hastily saying whether you are 
for or agin it. 

The deceptive thing about the little figure that is not there 
is that its absence so often goes unnoticed. That, of course, is 
the secret of its success. Critics of journalism as practised 
today have deplored the paucity of good old-fashioned leg 
work and spoken harshly of 'armchair correspondents', who 
live by uncritically re-writing government handouts. For a 
sample of unenterprising journalism take this item from a 
list of 'new industrial developments' in the news magazine 
Fortnight: 'a new cold temper bath which triples the hard- 
ness of steel, from Westinghouse'. 

Now that sounds like quite a development . . . until you 
try to put your finger on what it means. And then it becomes 
as elusive as a ball of quicksilver. Does the new bath make 
just any kind of steel three times as hard as it was before 
treatment? Or does it produce a steel three times as hard as 
any previous steel? Or what does it do? It appears that the 
reporter has passed along some words without inquiring 
what they mean, and you are expected to read them just as 

46 How to Lie with Statistics 

uncritically for the happy illusion they give you of having 
learned something. It is all too reminiscent of an old 
definition of the lecture method of classroom instruction: a 
process by which the contents of the textbook of the in- 
structor are transferred to the notebook of the student with- 
out passing through the heads of either party. 

A few minutes ago, while looking up something about Dr 
Kinsey in Time, I came upon another of those statements 
that collapse under a second look. It appeared in an adver- 
tisement by a group of electric companies in 1948. 'Today, 
electric power is available to more than three-quarters of 
U.S. farms. . . .' That sounds pretty good. Those power 
companies are really on the job. Of course, if you wanted to 
be ornery you could paraphrase it into 'Almost one-quarter 
of U.S. farms do not have electric power available today.' 
The real gimmick, however, is in that word 'available', and 
by using it the companies have been able to say just about 
anything they please. Obviously this does not mean that all 
those farmers actually have power, or the advertisement 
surely would have said so. They merely have it 'available' - 
and that, for all I know, could mean that the power lines go 
past their farms or merely within ten or a hundred miles of 

Let me quote a title from an article published in a popular 
magazine: 'You Can Tell Now how tall your child 
will grow.' With the article is conspicuously displayed a 
pair of charts, one for boys and one for girls, showing what 
percentage of his ultimate height a child reaches at each 
year of age. 'To determine your child's height at maturity,' 
says a caption, 'check present measurement against 

The funny thing about this is that the article itself - if you 
read on - tells you what the fatal weakness in the chart is. 
Not all children grow in the same way. Some start slowly 

48 How to Lie with Statistics 

and then speed up; others shoot up quickly for a while, then 
level off slowly; for still others growth is a relatively 
steady process. The chart, as you might guess, is based on 
averages taken from a large number of measurements. For 
the total, or average, heights of a hundred youngsters taken 
at random it is no doubt accurate enough, but a parent is 
interested in only one height at a time, a purpose for which 
such a chart is virtually worthless. If you wish to know how 
tall your child is going to be, you can probably make a better 

guess by taking a look at his parents and grandparents. That 
method isn't scientific and precise like the chart, but it is at 
least as accurate. 

I am amused to note that, taking my height as recorded 
when I enrolled in high-school military training at fourteen 
and ended up in the rear rank of the smallest squad, I should 
eventually have grown to a bare five feet eight. I am five feet 
eleven. A three-inch error in human height comes down to a 
poor grade of guess. 

The Little Figures That Are Not There 49 

Before me are wrappers from two boxes of Grape-Nuts 
Flakes. They are slightly different editions, as indicated by 
their testimonials: one cites Two-Gun Pete and the other 
says, 'If you want to be like Hoppy . . . you've got to eat like 
Hoppy!' Both offer charts to show ('Scientists proved it's 
true!') that these flakes 'start giving you energy in 2 
minutes!' In one case the chart hidden in these forests of 
exclamation points has numbers up the side; in the other 
case the numbers have been omitted. This is just as well, 

Time of eating 1 minute later 2 minutes later 


Time of eating 1 minute later 2 minutes later 

since there is no hint of what the numbers mean. Both show 
a steeply climbing red line ('energy release'), but one has it 
starting one minute after eating Grape-Nuts Flakes, the other 
two minutes later. One line climbs about twice as fast as the 
other, too, suggesting that even the draughtsman didn't 
think these graphs meant anything. 

Such foolishness could be found only on material meant 
for the eye of a juvenile or his morning-weary parent, of 
course. No one would insult a big businessman's intelligence 
with such statistical tripe ... or would he? Let me tell you 

So How to lie with Statistics 

about a graph used to advertise an advertising agency (I 
hope this isn't getting confusing) in the rather special 
columns of Fortune magazine. The line on this graph 
showed the impressive upward trend of the agency's 
business year by year. There were no numbers. With equal 
honesty this chart could have represented a tremendous 

1923 1924 1925 1926 1927 1928 1929 1930 1931 

growth, with business doubling or increasing by millions of 
dollars a year, or the snail-like progress of a static concern 
adding only a dollar or two to its annual billings. It made a 
striking picture, though. 

Place little faith in an average or a graph or a trend when 
those important figures are missing. Otherwise you are as 
blind as a man choosing a camp site from a report of mean 
temperature alone. You might take 61 degrees as a comfort- 
able annual mean, giving you a choice in California between 
such areas as the inland desert and San Nicolas Island off the 
south coast. But you can freeze or roast if you ignore the 
range. For San Nicolas it is 47 to 87 degrees but for the desert 
it is 15 to 104. 

The Little Figures That Are Not There 51 

Oklahoma City can claim a similar average temperature 
for the last sixty years: 602 degrees. But as you can see from 
the chart below, that cool and comfortable figure conceals a 
range of 130 degrees. 


Record temperatures in Oklahoma City 














S ^ 








Much Ado 
about Practically 

Sir Josiah Stamp has described an occasion when Lord Ran- 
dolph was examining a report of revenue. His private sec- 
retary was looking over his shoulder. Randolph remarked 
that it was gratifying to find customs revenue up 34 per cent 
over a corresponding period of the previous year. 

The secretary corrected him, pointing out that it was only 
•34 per cent. 

'What difference does that make?' Lord Randolph 

When it had been explained that one figure was a hundred 
times the other, Randolph said, 'I have often seen those 
damned little dots before, but I never knew until now what 
they meant.' 

Not dots but other damned little differences crop up to 
plague comparisons of test scores. To see how this is, we will 

Much ado about Practically Nothing 53 

begin - if you don't mind - by endowing you with two 
children. Peter and Linda (we might as well give them 
modish names while we're about it) have been given intelli- 
gence tests, as a great many children are in the course of 
their schooling. Now the mental test of any variety is one 
of the prime voodoo fetishes of our time, so you may have 
to argue a little to find out the results of the tests; this is 
information so esoteric that it is often held to be safe only in 
the hands of psychologists and educators, and they may be 
right at that. Anyway, you learn somehow that Peter's IQ is 
98 and Linda's is 101. You know, of course, that the IQ is 
based on 100 as average or 'normal'. 

Aha. Linda is your brighter child. She is, furthermore, 
above average. Peter is below average, but let's not dwell on 

Any such conclusions as these are sheer nonsense. 

Just to clear the air, let's note first of all that whatever an 
intelligence test measures it is not quite the same thing as we 
usually mean by intelligence. It neglects such important 
things as leadership and creative imagination. It takes no 
account of social judgement or musical or artistic or other 
aptitudes, to say nothing of such personality matters as dil- 
igence and emotional balance. On top of that, the tests most 
often given in schools are the quick-and-cheap group kind 
that depend a good deal upon reading facility; bright or not, 
the poor reader hasn't a chance. 

Let's say that we have recognized all that and agree to 
regard the IQ simply as a measure of some vaguely defined 
capacity to handle canned abstractions. And Peter and Linda 
have been given what is generally regarded as the best of the 
tests, the Revised Stanford-Binet, which is administered 
individually and doesn't call for any particular reading 

Now what an IQ test purports to be is a sampling of the 

54 How to Lie with Statistics 

intellect. Like any other product of the sampling method, 
the IQ is a figure with a statistical error, which expresses the 
precision or reliability of that figure. 

Asking these test questions is something like what you 
might do in estimating the quality of the maize in a field by 
going about and pulling off an ear here and an ear there at 
random. By the time you had stripped down and looked at a 
hundred ears, say, you would have gained a pretty good idea 
of what the whole field was like. Your information would be 
exact enough for use in comparing this field with another 
field - provided the two fields were not very similar. If 
they were, you might have to look at many more ears, 
rating them all the while by some precise standard of 

How accurately your sample can be taken to represent 
the whole field is a measure that can be represented in 
figures: the probable error and the standard error. 

Suppose that you had the task of measuring the size of a 
good many fields by pacing off the fence lines. The first thing 
you might do is check the accuracy of your measuring 
system by pacing off what you took to be a hundred yards, 
doing this a number of times. You might find that on the 
average you were off by three yards. That is, you came 
within three yards of hitting the exact one hundred in half 
your trials, and in the other half of them you missed by 
more than three yards. 

Your probable error then would be three yards in one 
hundred, or three per cent. From then on, each fence line 
that measured one hundred yards by your pacing might be 
recorded as ioo ± 3 yards. 

(Most statisticians now prefer to use another, but com- 
parable, measurement called the standard error. It takes in 
about two-thirds of the cases instead of exactly half and is 
considerably handier in a mathematical way. For our pur- 

Much ado about Practically Nothing 55 

poses we can stick to the probable error, which is the one 
still used in connection with the Stanford-Binet.) 

As with our hypothetical pacing, the probable error of the 
Stanford-Binet IQ has been found to be three per cent. This 
has nothing to do with how good the test is basically, only 
with how consistently it measures whatever it measures. So 
Peter's indicated IQ might be more fully expressed as 98 ± 
3 and Linda's as 101 =*= 3. 

This says that there is no more than an even chance that 
Peter's IQ falls anywhere between 95 and 101; it is just as 
likely that it is above or below that figure. Similarly Linda's 
has no better than a fifty-fifty probability of being within 
the range of 98 to 104. From this you can quickly see that 
there is one chance in four that Peter's IQ is really above 101 
and a similar chance that Linda's is below 98. Then Peter is 
not inferior but superior, and by a margin of anywhere from 
three points up. 

What this comes down to is that the only way to think 
about IQs and many other sampling results is in ranges. 
'Normal' is not 100, but the range of 90 to no, say, and 
there would be some point in comparing a child in this range 
with a child in a lower or higher range. But comparisons 
between figures with small differences are meaningless. You 
must always keep that plus-or-minus in mind, even (or es- 
pecially) when it is not stated. 

Ignoring these errors, which are implicit in all sampling 
studies, has led to some remarkably silly behaviour. There 
are magazine editors to whom readership surveys are gospel, 
mainly because they do not understand them. With forty 
per cent male readership reported for one article and only 
thirty-five per cent for another, they demand more articles 
like the first. 

The difference between thirty-five and forty per cent read- 
ership can be of importance to a magazine, but a survey 

56 How to Lie with Statistics 

difference may not be a real one. Costs often hold readership 
samples down to a few hundred persons, particularly after 
those who do not read the magazine at all have been elimi- 
nated. For a magazine that appeals primarily to women the 
number of men in the sample may be very small. By the 
time these have been divided among those who say they 'read 
all', 'read most', 'read some', or 'didn't read' the article in 
question, the thirty-five per cent conclusion may be based on 
only a handful. The probable error hidden behind the im- 
pressively presented figure may be so large that the editor 
who relies on it is grasping at a thin straw. 

Sometimes the big ado is made about a difference that is 
mathematically real and demonstrable but so tiny as to have 
no importance. This is in defiance of the fine old saying that 
a difference is a difference only if it makes a difference. A 
case in point is the hullabaloo over practically nothing that 
was raised so effectively, and so profitably, by the Old Gold 
cigarette people. 

It started innocently with the editor of the Reader's 
Digest, who smokes cigarettes but takes a dim view of them 
all the same. His magazine went to work and had a battery 
of laboratory folk analyse the smoke from several brands of 
cigarettes. The magazine published the results, giving the 
nicotine and whatnot content of the smoke by brands. The 
conclusion stated by the magazine and borne out in its de- 
tailed figures was that all the brands were virtually identical 
and that it didn't make any difference which one you 

Now you might think this was a blow to cigarette manu- 
facturers and to the fellows who think up the new copy 
angles in the advertising agencies. It would seem to explode 
all advertising claims about soothing throats and kindness to 

But somebody spotted something. In the lists of almost 

Much ado about Practically Nothing 57 

identical amounts of poisons, one cigarette had to be at the 
bottom, and the one was Old Gold. Out went the telegrams, 
and big advertisements appeared in newspapers at once in 
the biggest type at hand. The headlines and the copy simply 
said that of all cigarettes tested by this great national maga- 
zine Old Gold had the least of these undesirable things in its 
smoke. Excluded were all figures and any hint that the 
difference was negligible. 

In the end, the Old Gold people were ordered to 'cease and 
desist' from such misleading advertising. That didn't make 
any difference; the good had been milked from the idea long 





There is terror in numbers. Humpty Dumpty's confidence in 
telling Alice that he was master of the words he used would 
not be extended by many people to numbers. Perhaps we 
suffer from a trauma induced by early experiences with 

Whatever the cause, it creates a real problem for the 
writer who yearns to be read, the advertising man who 
expects his copy to sell goods, the publisher who wants his 
books or magazines to be popular. When numbers in tabular 
form are taboo and words will not do the work well, as is 
often the case, there is one answer left: Draw a picture. 

About the simplest kind of statistical picture, or graph, is 
the line variety. It is very useful for showing trends, some- 
thing practically everybody is interested in showing or 
knowing about or spotting or deploring or forecasting. 

The Gee-Whiz Graph 59 

We'll let our graph show how national income increased ten 
per cent in a year. 

Begin with paper ruled into squares. Name the months 
along the bottom. Indicate billions of dollars up the side. 
Plot your points and draw your line, and your graph will 
look like this: 













Now that's clear enough. It shows what happened during 
the year and it shows it month by month. He who runs may 
see and understand, because the whole graph is in pro- 
portion and there is a zero line at the bottom for com- 
parison. Your ten per cent looks like ten per cent - an 

6o How to Lie with Statistics 

upward trend that is substantial but perhaps not over- 

That is very well if all you want to do is convey infor- 
mation. But suppose you wish to win an argument, shock a 
reader, move him into action, sell him something. For that, 
this chart lacks schmaltz. Chop off the bottom. 






Now that's more like it. (You've saved paper too, something 
to point out if any carping fellow objects to your misleading 
graphics.) The figures are the same and so is the curve. It is 
the same graph. Nothing has been falsified - except the im- 
pression that it gives. But what the hasty reader sees now is a 
national-income line that has climbed half-way up the paper 
in twelve months, all because most of the chart isn't there 
any more. Like the missing parts of speech in sentences that 
you met in grammar classes, it is 'understood'. Of course, the 
eye doesn't 'understand' what isn't there, and a small rise has 
become, visually, a big one. 

Now that you have practised to deceive, why stop with 
truncating? You have a further trick available that's worth a 
dozen of that. It will make your modest rise of ten per cent 
look livelier than one hundred per cent is entitled to look. 
Simply change the proportion between the ordinate and the 
abscissa. There's no rule against it, and it does give your 
graph a prettier shape. AH you have to do is let each mark 

The Gee-Whiz Graph 61 

up the side stand for only one-tenth as many dollars as 

That is impressive, isn't it? Anyone looking at it can just feel 
prosperity throbbing in the arteries of the country. It is a 
subtler equivalent of editing 'National income rose ten per 
cent' into '. . . climbed a whopping ten per cent'. It is vastly 
more effective, however, because it contains no adjectives or 
adverbs to spoil the illusion of objectivity. There's nothing 
anyone can pin on you. 

And you're in good, or at least respectable, company. A 
news magazine has used this method to show the stock 
market hitting a new high, the graph being so truncated as 
to make the climb look far more dizzying than it was. A 

62 How to Lie with Statistics 

Columbia Gas System advertisement once reproduced a 
chart 'from our new Annual Report'. If you read the little 
numbers and analysed them you found that during a ten- 
year period living costs went up about sixty per cent and the 
cost of gas dropped four per cent. This is a favourable pic- 
ture, but it apparently was not favourable enough for 
Columbia Gas. They chopped off their chart at ninety per 
cent (with no gap or other indication to warn you) so that 
this was what your eye told you: Living costs have more 
than tripled, and gas has gone down one-third! 

Govt pay rolls up I 

Govt, pay rolls stable I 








J 20 









— *• 




i i 

1 < 

• * 

r 1 

i J 

; s 

: c 

\ j 

3 S 

c 8 

\ I 

i J 

i i 



Steel companies have used similarly misleading graphic 
methods in attempts to line up public opinion against wage 
increases. Yet the method is far from new, and its impro- 
priety was shown up long ago - not just in technical pub- 
lications for statisticians either. An editorial writer in Dun's 
Review back in 1938 reproduced a chart from an adver- 
tisement advocating advertising in Washington, D.C., the 
argument being nicely expressed in the headline over the 

The Gee-Whiz Graph 63 

chart: government pay rolls up! The line in the graph 
went along with the exclamation point even though the 
figures behind it did not. What they showed was an increase 
from about $19,500,000 to $20,200,000. But the red line shot 
from near the bottom of the graph clear to the top, making 
an increase of under four per cent look like more than 400. 
The magazine gave its own graphic version of the same 
figures alongside - an honest red line that rose just four per 
cent, under this caption: government pay rolls 





3,205,000 est 

First nine months 


Last quarter 

From a 24 April 1953, newspaper advertisement for Collier's. 





A generation or so ago we were hearing a good deal about 
the little people, meaning practically all of us. When this 
began to sound too condescending, we became the common 
man. Pretty soon that was forgotten too, which was prob- 
ably just as well. But the little man is still with us. He is the 
character on the chart. 

A chart on which a little man represents a million men, a 
moneybag or stack of coins a thousand pounds sterling or a 
million dollars, an outline of a steer your beef supply for 
next year, is a pictorial graph. It is a useful device. It has 
what I am afraid is known as eye-appeal. And it is capable 
of becoming a fluent, devious, and successful liar. 

The daddy of the pictorial chart, or pictograph, is the 
ordinary bar chart, a simple and popular method of rep- 
resenting quantities when two or more are to be compared. 

The One-Dimensional Picture 65 

A bar chart is capable of deceit too. Look with suspicion on 
any version in which the bars change their widths as well as 
their lengths while representing a single factor or in which 
they picture three-dimensional objects the volumes of which 
are not easy to compare. A truncated bar chart has, and 
deserves, exactly the same reputation as the truncated line 
graph we have been talking about. The habitat of the bar 
chart is the geography book, the corporation statement, and 
the news magazine. This is true also of its eye-appealing 

t « 

I 15 









:. -A 



Rotundia England 

Perhaps I wish to show a comparison of two figures - the 
average weekly wage of one kind of working man or 
another in England and Rotundia, let's say. The sums might 
be £30 and £15. 1 wish to catch your eye with this, so I am 
not satisfied merely to print the numbers. I make a bar chart. 
(By the way, if that £30 figure doesn't square with the huge 
sum you laid out when your porch needed a new railing last 
summer, remember that your man may not have done as 
well every week as he did while working for you. And 
anyway I didn't say what kind of average I have in mind or 
how I arrived at it. so it isn't going to get you anywhere to 

66 How to Lie with Statistics 

quibble. You see how easy it is to hide behind the most 
disreputable statistic if you don't include any other infor- 
mation with it? You probably guessed I just made this one 
up for purposes of illustration, but I'll bet you wouldn't 
have if I'd used £29.35 instead.) 

There it is, with pounds-per-week indicated up the left 
side. It is a clear and honest picture. Twice as much money 
is twice as big on the chart and looks it. 

The chart lacks that eye-appeal though, doesn't it? I can 
easily supply that by using something that looks more like 
money than a bar does: moneybags. One moneybag for the 
unfortunate Rotundian's pittance, two for the Englishman's 
wage. Or three for the Rotundian, six for the Englishman. 
Either way, the chart remains honest and clear, and it will 
not deceive your hasty glance. That is the way an honest 
pictograph is made. 

? 5 ^ Tc/ **&w- 

The One-Dimensional Picture 67 

That would satisfy me if all I wanted was to com- 
municate information. But I want more. I want to say that 
the English working man is vastly better off than the Rotun- 
dian, and the more I can dramatize the difference between 
fifteen and thirty the better it will be for my argument. To 
tell the truth (which, of course, is what I am planning not to 
do), I want you to infer something, to come away with an 
exaggerated impression, but I don't want to be caught at my 
tricks. There is a way, and it is one that is being used every 
day to fool you. 

I simply draw a moneybag to represent the Rotundian's 
£15, and then I draw another one twice as tall to represent 
the Englishman's £30. That's in proportion, isn't it? 

Now that gives the impression I'm after. The Englishman's 
wage now dwarfs the foreigner's. 

The catch, of course, is this. Because the second bag is 
twice as high as the first, it is also twice as wide. It occupies 
not twice but four times as much area on the page. The 
numbers still say two to one, but the visual impression, 
which is the dominating one most of the time, says the ratio 
is four to one. Or worse. Since these are pictures of objects 
having in reality three dimensions, the second must also be 
twice as thick as the first. As your geometry book put it, the 
volumes of similar solids vary as the cube of any like dim- 
ension. Two times two times two is eight. If one moneybag 
holds £i£, the other, having eight times the volume, must 
hold not £30 but £120. 

And that indeed is the impression my ingenious little 
chart gives. While saying 'twice', I have left the lasting im- 
pression of an overwhelming eight-to-one ratio. 

You'll have trouble pinning any criminal intent on me, 
too. I am only doing what a great many other people do. A 
leading news magazine has done it repeatedly, with money- 
bags just like those in our example. 

68 How to Lie with Statistics 

In America, the Iron and Steel Institute has done it, with a 
pair of blast furnaces. The idea was to show how the indus- 
try's steelmaking capacity had boomed between one decade 
and the next and so indicate that the industry was doing 
such a job on its own that any governmental interference 
was uncalled for. However shaky the thesis, it has more 

Steel capacity added 

_ t^ 

e 1930s = 

1 million tons 

Adapted by courtesy ot Steelways. 

14J million tons 

merit than there is in the way it was presented. The blast 
furnace representing the ten-million-ton capacity added in 
one decade was drawn just over two-thirds as tall as the 
furnace representing the fourteen and a quarter million tons 
added in the next. The eye saw two furnaces, one of them 
close to three times as big as the other. To say 'almost one 
and one-half and to be heard as 'three' - that's what the one 
dimensional picture can accomplish. 
This piece of art work by the steel people had some other 

The One-Dimensional "Picture 69 

points of interest. Somehow the second furnace had fattened 
out horizontally beyond the proportion of its neighbour, 
and a black bar, suggesting molten iron, had become two 
and one-half times as long as in the earlier decade. Here was 
a 50 per cent increase given, then drawn as 150 per cent to 
give a visual impression of - unless my slide rule and I are 
getting out of their depth - over 1,500 per cent. Arithmetic 
becomes fantasy. 

(It is almost too unkind to mention that the same glossy 
four-colour page offers a fair-to-prime specimen of the trun- 
cated line graph. A curve exaggerates the per-capita growth 
of steelmaking capacity by getting along with the lower half 
of its graph missing. This saves paper and doubles the rate of 

Some of this may be no more than sloppy draughts- 
manship. But it is rather like being short-changed: When all 
the mistakes are in the cashier's favour, you can't help won- 

Newsweek once showed how 'Old Folks Grow Older' by 
means of a chart on which appeared two male figures, one 
representing the 68-2-year life expectancy of today, the 
other the 34-year life expectancy of 1879-89. It was the 
same old story: One figure was twice as tall as the other and 
so would have had eight times the bulk or weight. This pic- 
ture sensationalized facts in order to make a better story. 
I would call it a form of yellow journalism. The same issue 
of the magazine contained a truncated, or gee-whiz, line 

There is still another kind of danger in varying the size of 
objects in a chart. It seems that in i860 there were some- 
thing over eight million milk cows in the United States and 
about a century later there were more than twenty-five 
million. Showing this increase by drawing two cows, one 
three times the height of the other, will exaggerate the 

The ciesdve cow 

1860 ^ 


The diminishing rhinoceros 


The One-Dimensional Picture 71 

impression in the manner we have been discussing. But the 
effect on the hasty scanner of the page may be even stranger: 
He may easily come away with the idea that cows are 
bigger now than they used to be. 

Apply the same deceptive technique to what has hap- 
pened to the rhinoceros population and this is what you get. 
Ogden Nash once rhymed rhinosterous with preposterous. 
That's the word for the method too. 







"When you are a bit older,' a judge in India once told an 
eager young British civil servant, 'you will not quote Indian 
statistics with that assurance. The government are very keen 
on amassing statistics - they collect them, add them, raise 
them to the nth power, take the cube root and prepare won- 
derful diagrams. But what you must never forget is that 
every one of those figures comes in the first instance from 
the chowty dar [village watchman], who just puts down 
what he damn pleases.' 

If you can't prove what you want to prove, demonstrate 
something else and pretend that they are the same thing. In 
the daze that follows the collision of statistics with the 
human mind, hardly anybody will notice the difference. The 
semi-attached figure is a device guaranteed to stand you in 
good stead. It always has. 

The Semi-attached Figure 73 

You can't prove that your nostrum cures colds, but you 
can publish (in large type) a sworn laboratory report that 
half an ounce of the stuff killed 31,108 germs in a test tube in 
eleven seconds. While you are about it, make sure that the 
laboratory is reputable or has an impressive name. Repro- 
duce the report in full. Photograph a doctor-type model in 
white clothes and put his picture alongside. 

***** j»to}dljL 

But don't mention the several gimmicks in your story. It is 
not up to you - is it? - to point out that an antiseptic that 
works well in a test tube may not perform in the human 
throat, especially after it has been diluted according to in- 
structions to keep it from burning throat tissue. Don't con- 
fuse the issue by telling what kind of germ you killed. Who 
knows what germ causes colds, particularly since it prob- 
ably isn't a germ at all? 

In fact, there is no known connection between assorted 

74 How to Lie with Statistics 

germs in a test tube and the whatever-it-is that produces 
colds, but people aren't going to reason that sharply, es- 
pecially while sniffling. 

Maybe that one is too obvious, and people are beginning 
to catch on, although it would not appear so from the adver- 
tising pages. Anyway, here is a trickier version. 

Let us say that during a period in which race prejudice is 
growing you are employed to 'prove' otherwise. It is not a 
difficult assignment. Set up a poll or, better yet, have the 
polling done for you by an organization of good reputation. 
Ask that usual cross section of the population if they think 
black people have as good a chance as white people to get 
jobs. Repeat your polling at intervals so that you will have a 
trend to report. 

Princeton's Office of Public Opinion Research tested this 
question once. What turned up is interesting evidence that 
things, especially in opinion polls, are not always what they 
seem. Each person who was asked the question about jobs 
was also asked some questions designed to discover if he was 
strongly prejudiced against blacks. It turned out that people 
most strongly prejudiced were most likely to answer Yes to 
the question about job opportunities. (It worked out that 
about two-thirds of those who were sympathetic towards 
Negroes did not think the Negro had as good a chance at a 
job as a white person did, and about two-thirds of those 
showing prejudice said that blacks were getting as good 
breaks as whites.) It was pretty evident that from this poll 
you would learn very little about employment conditions 
for Negroes, although you might learn some interesting 
things about a man's racial attitudes. 

You can see, then, that if prejudice is mounting during 
your polling period you will get an increasing number of 
answers to the effect that Negroes have as good a chance at 
jobs as whites. So you announce your results: Your 

The Semi-attached Figure 75 

poll shows that blacks are getting a fairer shake all the 

You have achieved something remarkable by careful use 
of a semi-attached figure. The worse things get, the better 
your poll makes them look. 

Or take this one: '27 per cent of a large sample of eminent 
physicians smoke Throaties - more than any other brand.' 
The figure itself may be phoney, of course, in any of several 




ways, but that really doesn't make any difference. The only 
answer to a figure so irrelevant is 'So what?' With all proper 
respect towards the medical profession, do doctors know 
any more about tobacco brands than you do? Do they have 
any inside information that permits them to choose the least 
harmful among cigarettes? Of course they don't, and your 
doctor would be the first to say so. Yet that '27 per cent' 
somehow manages to sound as if it meant something. 

jd How to Lie with Statistics 

Now slip back one percentage point and consider the case 
of the juice extractor. It was widely advertised as a device 
that 'extracts 26 per cent more juice* as 'proved by lab- 
oratory test' and 'vouched for by Good Housekeeping Insti- 

That sounds right good. If you can buy a juicer that is 
twenty-six per cent more effective, why buy any other kind? 
Well now, without going into the fact that 'laboratory tests' 
(especially 'independent laboratory tests') have proved some 
of the darndest things, just what does that figure mean? 
Twenty-six per cent more than what? When it was finally 
pinned down it was found to mean only that this juicer got 
out that much more juice than an old-fashioned hand 
reamer could. It had absolutely nothing to do with the data 
you would want before purchasing; this juicer might be the 
poorest on the market. Besides being suspiciously precise, 
that twenty-six per cent figure is totally irrelevant. 

Advertisers aren't the only people who will fool you with 
numbers if you let them. An article on driving safety, pub- 
lished by This Week magazine undoubtedly with your best 
interests at heart, told you what might happen to you if you 
went 'hurtling down the highway at 70 miles an hour, 
careering from side to side.' You would have, the article said, 
four times as good a chance of staying alive if the time were 
seven in the morning than if it were seven at night. The 
evidence: 'Four times more fatalities occur on the highways 
at 7 p.m. than at 7 a.m.' Now that is approximately true, but 
the conclusion doesn't follow. More people are killed in the 
evening than in the morning mainly because more people 
are on the highways then to be killed. You, a single driver, 
may be in greater danger in the evening, but there is nothing 
in the figures to prove it either way. 

By the same kind of nonsense that the article writer used 
you can show that clear weather is more dangerous than 

The Semi-attached Figure jj 

foggy weather. More accidents occur in clear weather, be- 
cause there is more clear weather than foggy weather. All 
the same, fog may be much more dangerous to drive in. 

You can use accident statistics to scare yourself to death 
in connection with any kind of transportation ... if you 
fail to note how poorly attached the figures are. 

More people were killed by aeroplanes last year than in 
1910. Therefore modern planes are more dangerous? Non- 
sense. There are hundreds of times more people flying now, 
that's all. 

It was reported that the number of deaths chargeable to 
railroads in one year was 4,7i2.That sounds like a good argu- 
ment for staying off trains, perhaps for sticking to your auto- 
mobile instead. But when you investigate to find what the 
figure is all about, you learn it means something quite 
different. Nearly half those victims were people whose auto- 
mobiles collided with trains at crossings. The greater part of 
the rest were riding the rods. Only 132 out of the 4,712 were 
passengers on trains. And even that figure is worth little for 
purposes of comparison unless it is attached to information 
on total passenger miles. 

If you are worried about your chances of being killed on a 
coast-to-coast trip, you won't get much relevant infor- 
mation by asking whether trains, planes, or cars killed the 
greatest number of people last year. Get the rate, by in- 
quiring into the number of fatalities for each million passen- 
ger miles. That will come closest to telling you where your 
greatest risk lies. 

There are many other forms of counting up something 
and then reporting it as something else. The general method 
is to pick two things that sound the same but are not. As 
personnel manager for a company that is scrapping with a 
union you 'make a survey' of employees to find out how 
many have a complaint against the union. Unless the union 

78 How to Lie with Statistics 

is a band of angels with an archangel at their head you can 
ask and record with perfect honesty and come out with 
proof that the greater part of the men do have some com- 
plaint or other. You issue your information as a report that 'a 
vast majority - 78 per cent - are opposed to the union.' 
What you have done is to add up a bunch of un- 
differentiated complaints and tiny gripes and then call 
them something else that sounds like the same thing. You 
haven't proved a thing, but it rather sounds as if you have, 
doesn't it? 

It is fair enough, though, in a way. The union can just as 
readily 'prove' that practically all the workers object to the 
way the plant is being run. 

If you'd like to go on a hunt for semi-attached figures, you 
might try running through corporation financial statements. 
Watch for profits that might look too big and so are 
concealed under another name. The United Automobile 
Workers' magazine Ammunition describes the device this 

The statement says, last year the company made $35 million 
in profits. Just one and a half cents out of every sales dollar. You 
feel sorry for the company. A bulb burns out in the latrine. To 
replace it, the company has to spend 30 cents. Just like that, 
there is the profit on 20 sales dollars. Makes a man want to go 
easy on the paper towels. 

But, of course, the truth is, what the company reports as 
profits is only a half or a third of the profits. The part that isn't 
reported is hidden in depreciation, and special depreciation, and 
in reserves for contingencies. 

Equally gay fun is to be had with percentages. For a nine- 
month period General Motors was able to report a relatively 
modest profit (after taxes) of 126 per cent on sales. But for 
that same period GM's profit on its investment came to 448 
per cent, which sounds a good deal worse - or better, de- 

The Semi-attached Figure 79 

pending on what kind of argument you are trying to win. 

Similarly, a reader of Harper's magazine came to the de- 
fence of the A & P stores in that magazine's letters column 
by pointing to low net earnings of only i-i per cent of sales. 
He asked, 'Would any American citizen fear public con- 
demnation as a profiteer . . . for realizing a little over $10 
for every $1,000 invested during a year?" 

Offhand this i-i per cent sounds almost distressingly 
small. Compare it with the six per cent or more interest that 
most of us are familiar with from home mortgages and bank 
loans and such. Wouldn't the A & P be better off if it went 
out of the grocery business and put its capital into the bank 
and lived off interest? 

The catch is that annual return on investment is not the 
same kettle of fish as earnings on total sales. As another 
reader replied in a later issue of Harper's, 'If I purchase an 
article every morning for 99 cents and sell it each afternoon 
for one dollar, I will make only 1 per cent on total sales, but 
365 per cent on invested money during the year.' 

There are often many ways of expressing any figure. You 
can, for instance, express exactly the same fact by calling it 
a one per cent return on sales, a fifteen per cent return on 
investment, a ten-million-dollar profit, an increase in profits 
of forty per cent (compared with 1965-9 average), or a de- 
crease of sixty per cent from last year. The method is to 
choose the one that sounds best for the purpose at hand and 
trust that few who read it will recognize how imperfectly it 
reflects the situation. 

Not all semi-attached figures are products of intentional 
deception. Many statistics, including medical ones that are 
pretty important to everybody, are distorted by inconsistent 
reporting at the source. There are startlingly contradictory 
figures on such delicate matters as abortions, illegitimate 
births, and syphilis. If you should look up the latest avail- 

80 How to Lie with Statistics 

able figures on influenza and pneumonia in the United 
States, you might come to the strange conclusion that these 
ailments are practically confined to three southern states, 
which account for about eighty per cent of the reported 
cases. What actually explains this percentage is the fact that 
these three states required reporting of the ailments after 
other states had stopped doing so. 

Some malaria figures mean as little. Where before 1940 
there were hundreds of thousands of cases a year in the 
American South there are now only a handful, a salubrious 
and apparently important change that took place in just a 
few years. But all that has happened in actuality is that cases 
are now recorded only when proved to be malaria, where 
formerly the word was used in much of the South as a col- 
loquialism for a cold or chill. 

The death rate in the Navy during the Spanish-American 
War was nine per thousand. For civilians in New York City 
during the same period it was sixteen per thousand. Navy 
recruiters later used these figures to show that it was safer to 

The Semi-attached Figure 81 

be in the US. Navy than out of it. Assume these figures to be 
accurate, as they probably are. Stop for a moment and see if 
you can spot what makes them, or at least the conclusion 
the recruiting people drew from them, virtually mean- 

The groups are not comparable. The Navy is made up 
mainly of young men in known good health. A civilian 
population includes infants, the old, and the ill, all of whom 
have a higher death rate wherever they are. These figures do 
not at all prove that men meeting Navy standards will live 
longer in the Navy than out. They do not prove the contrary 

Shortly before polio vaccines came along we were hit by 
the discouraging news that the previous year had been the 
worst in history for polio. This conclusion was based on 
what might seem all the evidence anyone could ask for: 
There were far more cases reported in that year than ever 

But when experts went back of these figures they found a 
few things that were more encouraging. One was that there 
were so many more children at the most susceptible ages 
than ever before that cases were bound to be at a record 
number if the rate remained level. Another was that a gen- 
eral consciousness of polio was leading to more frequent 
diagnoses and recording of mild cases. Finally, there was an 
increased financial incentive, there being more polio in- 
surance and more aid available from charitable organi- 
zations. All this threw considerable doubt on the notion 
that polio had reached a new high, and the total number of 
deaths confirmed the doubt. 

It is an interesting fact that the death rate or number of 
deaths often is a better measure of the incidence of an ail- 
ment than direct incidence figures - simply because the qual- 
ity of reporting and record-keeping is so much higher on 

82 How to Lie with Statistics 

fatalities. In this instance, the obviously semi-attached figure 
is better than the one that on the face of it seems fully at- 

In America the semi-attached figure enjoys a big boom 
every fourth year. This indicates not that the figure is cyc- 
lical in nature, but only that campaign time has arrived. A 
campaign statement issued by the Republican party in 
October of 1948 is built entirely on figures that appear to be 
attached to each other but are not: 

When Dewey was elected Governor in 1942, the minimum 
teacher's salary in some districts was as low as $900 a year. 
Today the school teachers in New York State enjoy the highest 
salaries in the world. Upon Governor Dewey's recommen- 
dation, based on the findings of a Committee he appointed, the 
Legislature in 1947 appropriated $32,000,000 out of a state 
surplus to provide an immediate increase in the salaries of 
school teachers. As a result the minimum salaries of teachers in 
New York City range from $2,500 to $5,325. 

It is entirely possible that Mr Dewey has proved himself 
the teacher's friend, but these figures don't show it. It is the 
old before-and-after trick, with a number of unmentioned 
factors introduced and made to appear what they are not. 
Here you have a 'before' of $900 and an 'after' of $2,500 to 
$5,325, which sounds like an improvement indeed. But the 
small figure is the lowest salary in any rural district of the 
state, and the big one is the range in New York City alone. 
There may have been an improvement under Governor 
Dewey, and there may not. 

This statement illustrates a statistical form of the before- 
and-after photograph that is a familiar stunt in magazines 
and advertising. A living-room is photographed twice to 
show you what a vast improvement a coat of paint can 
make. But between the two exposures new furniture has 
been added, and sometimes the 'before' picture isa tiny one in 

The Semi-attached Figure 83 

poorly lighted black-and-white and the 'after' version is a 
big photograph in full colour. Or a pair of pictures shows 
you what happened when a girl began to use a hair rinse. By 
golly, she does look better afterwards at that. But most 
of the change, you note on careful inspection, has been 
wrought by persuading her to smile and throwing a back 
light on her hair. More credit belongs to the photographer 
than to the rinse. 



8 ^ 

Post Hoc 
Rides Again 

You can make an estimate - one that is better than chance 
would produce - of how many children have been born into 
a Dutch or Danish family by counting the storks' nests on 
the roof of their house. 

In statistical terminology it would be said that a positive 
correlation has been found to exist between these two 

What sounds like proof of an ancient myth is actually 
something far more valuable. It is an easily remembered re- 
minder of a useful truth: an association between two factors 
is not proof that one has caused the other. 

In the instance of the storks and the babies, it is not too 
hard to find a third factor that may be responsible for the 
other two. Big houses attract big, and potentially big, fami- 
lies; and big houses have more chimney pots on which 
storks may nest. 

Tost Hoc Rides Again 85 

But flaws in assumptions of causality are not always so 
easy to spot, especially when the relationship seems to make 
a lot of sense or when it pleases a popular prejudice. 

Somebody once went to a good deal of trouble to find out 
if cigarette smokers make lower college grades than non- 
smokers. It turned out that they did. This pleased a good 
many people and they have been making much of it ever 
since. The road to good grades, it would appear, lies in 
giving up smoking; and, to carry the conclusion one reason- 
able step further, smoking makes dull minds. 

This particular study was, I believe, properly done: 
sample big enough and honestly and carefully chosen, cor- 
relation having a high significance, and so on. 

The fallacy is an ancient one which, however, has a 
powerful tendency to crop up in statistical material, where 
it is disguised by a welter of impressive figures. It is the one 
that says that if B follows A, then A has caused B. An un- 
warranted assumption is being made that since smoking and 
low grades go together, smoking causes low grades. Couldn't 
it just as well be the other way around? Perhaps low marks 
drive students not to drink but to tobacco. When it comes 
right down to it, this conclusion is about as likely as the 
other and just as well supported by the evidence. But it is 
not nearly so satisfactory to propagandists. 

It seems a good deal more probable, however, that neither 
of these things has produced the other, but both are a pro- 
duct of some third factor. Can it be that the sociable sort of 
fellow who takes his books less than seriously is also likely 
to smoke more? Or is there a clue in the fact that somebody 
once established a correlation between extroversion and low 
grades - a closer relationship apparently than the one be- 
tween grades and intelligence? Maybe extroverts smoke 
more than introverts. The point is that when there are many 
reasonable explanations you are hardly entitled to pick 

86 How to Lie with Statistics 

one that suits your taste and insist on it. But many people 

To avoid falling for the post hoc fallacy and thus wind up 
believing many things that are not so, you need to put any 
statement of relationship through a sharp inspection. The 
correlation, that convincingly precise figure that seems to 
prove that something is because of something, can actually 
be any of several types. 

One is the correlation produced by chance. You may be 
able to get together a set of figures to prove some unlikely 
thing in this way, but if you try again, your next set may 
not prove it at all. As with the manufacturer of the tooth 
paste that appeared to reduce decay, you simply throw 
away the results you don't want and publish widely those 
you do. Given a small sample, you are likely to find some 
substantial correlation between any pair of characteristics 
or events that you can think of. 

A common kind of co-variation is one in which the re- 
lationship is real but it is not possible to be sure which of the 
variables is the cause and which the effect. In some of these 
instances cause and effect may change places from time to 
time or indeed both may be cause and effect at the same 
time. A correlation between income and ownership of 
stocks might be of that kind. The more money you make, 
the more stock you buy, and the more stock you buy, the 
more income you get; it is not accurate to say simply that 
one has produced the other. 

Perhaps the trickiest of them all is the very common in- 
stance in which neither of the variables has any effect at all 
on the other, yet there is a real correlation. A good deal of 
dirty work has been done with this one. The poor grades 
among cigarette smokers is in this category, as are all too 
many medical statistics that are quoted without the 
qualification that although the relationship has been shown 

Post Hoc Rides Again 87 

to be real, the cause-and-effect nature of it is only a matter of 
speculation. As an instance of the nonsense or spurious cor- 
relation that is a real statistical fact, someone has gleefully 
pointed to this: There is a close relationship between the 
salaries of Presbyterian ministers in Massachusetts and the 
price of rum in Havana. 

Which is the cause and which the effect? In other words, 
are the ministers benefiting from the rum trade or sup- 
porting it? All right. That's so farfetched that it is ridiculous 
at a glance. But watch out for other applications of post hoc 
logic that differ from this one only in being more subtle. In 
the case of the ministers and the rum it is easy to see that 
both figures are growing because of the influence of a third 
factor: the historic and world-wide rise in the price level of 
practically everything. 

And take the figures that show the suicide rate to be at its 
maximum in June. Do suicides produce June brides - or do 
June weddings precipitate suicides of the jilted? A somewhat 
more convincing (though equally unproved) explanation is 
that the fellow who licks his depression all through the 
winter with the thought that things will look rosier in the 
spring gives up when June comes and he still feels terrible. 

Another thing to watch out for is a conclusion in which a 
correlation has been inferred to continue beyond the data 
with which it has been demonstrated. It is easy to show that 
the more it rains in an area, the taller the corn grows or even 
the greater the crop. Rain, it seems, is a blessing. But a season 
of very heavy rainfall may damage or even ruin the crop. 
The positive correlation holds up to a point and then quickly 
becomes a negative one. Above so-many inches, the more it 
rains the less corn you get. 

A correlation of course shows a tendency which is not 
often the ideal relationship described as one-to-one. Tall 
boys weigh more than short boys on the average, so this is a 

88 How to Lie with Statistics 

positive correlation. But you can easily find a six-footer who 
weighs less than some five-footers, so the correlation is less 
than i. A negative correlation is simply a statement that as 
one variable increases the other tends to decrease. In physics 

this becomes an inverse ratio: The further you get from a 
light bulb the less light there is on your book; as distance 
increases light intensity decreases. These physical relation- 
ships often have the kindness to produce perfect correlations, 
but figures from business or sociology or medicine seldom 
work out so neatly. Even if education generally increases 
incomes it may easily turn out to be the financial ruination 
of Joe over there. Keep in mind that a correlation may be 
real and based on real cause and effect - and still be almost 
worthless in determining action in any single case. 

Post Hoc Bides Again 89 

Reams of pages of figures have been collected to show the 
value in dollars of a college education, and stacks of pam- 
phlets have been published to bring these figures - and con- 
clusions more or less based on them - to the attention of 
potential students. I am not quarrelling with the intention. I 
am in favour of education myself, particularly if it in- 
cludes a course in elementary statistics. Now these figures 
have pretty conclusively demonstrated that people who 
have gone to college make more money than people 
who have not. The exceptions are numerous, of course, but 
the tendency is strong and clear. 

The only thing wrong is that along with the figures and 
facts goes a totally unwarranted conclusion. This is the post 
hoc fallacy at its best. It says that these figures show that if 
you (your son, your daughter) attend college you will prob- 
ably earn more money than if you decide to spend the next 
four years in some other manner. This unwarranted conclu- 
sion has for its basis the equally unwarranted assump- 
tion that since college-trained folks make more money, they 
make it because they went to college. Actually we don't 
know but that these are the people who would have made 
more money even if they had not gone to college. There are 
a couple of things that indicate rather strongly that this is 
so. Colleges get a disproportionate number of two groups of 
kids: the bright and the rich. The bright might show good 
earning power without college knowledge. And as for the 
rich ones . . . well, money breeds money in several obvious 
ways. Few sons of rich men are found in low-income brack- 
ets whether they go to college or not. 

The following passage is taken from an article in question- 
and-answer form that appeared in a Sunday newspaper of 
enormous circulation. Maybe you will find it amusing, as I 
do, that the same writer once produced a piece called 'Popu- 
lar Notions: True or False?' 

90 How to Lie with Statistics 

q: What effect does going to college have on your chances of 
remaining unmarried? 

a: If you're a woman, it skyrockets your chances of becoming 
an old maid. But if you're a man, it has the opposite effect - it 
minimizes your chances of staying a bachelor. 

Cornell University made a study of 1,500 typical middle-aged 
college graduates. Of the men, 93 per cent were married (com- 
pared to 83 per cent for the general population). 

But of the middle-aged women graduates only 65 per cent 
were married. Spinsters were relatively three times as numerous 
among college graduates as among women of the general popu- 

When Susie Brown, age seventeen, reads this she learns 
that if she goes to college she will be less likely to get a man 
than if she doesn't. That is what the article says, and there 
are statistics from a reputable source to go with it. They go 
with it, but they don't back it up; and note also that while 
the statistics are Cornell's the conclusions are not, although 
a hasty reader may come away with the idea that they 

Here again a real correlation has been used to bolster up 
an unproved cause-and-effect relationship. Perhaps it all 
works the other way around and those women would have 
remained unmarried even if they had not gone to college. 
Possibly even more would have failed to marry. If these 
possibilities are no better than the one the writer insists 
upon, they are perhaps just as valid conclusions: that is, 

Indeed there is one piece of evidence suggesting that a 
propensity for old-maidhood may lead to going to college. 
Dr Kinsey seems to have found some correlation between 
sexuality and education, with traits perhaps being fixed at 
pre-college age. That makes it all the more questionable to 
say that going to college gets in the way of marrying. 

Tost Hoc Rides Again 91 

Note to Susie Brown: It ain't necessarily so. 

A medical article once pointed with great alarm to an 
increase in cancer among milk drinkers. Cancer, it seems, 
was becoming increasingly frequent in New England, Min- 
nesota, Wisconsin, and Switzerland, where a lot of milk is 
produced and consumed, while remaining rare in Ceylon, 
where milk is scarce. For further evidence it was pointed out 
that cancer was less frequent in some Southern states where 
less milk was consumed. Also, it was pointed out, milk- 
drinking English women get some kinds of cancer eighteen 
times as frequently as Japanese women who seldom drink 

A little digging might uncover quite a number of ways to 
account for these figures, but one factor is enough by itself 
to show them up. Cancer is predominantly a disease that 
strikes in middle life or after. Switzerland and the states 
mentioned first are alike in having populations with rela- 
tively long spans of life. English women at the time the 
study was made were living an average of twelve years 
longer than Japanese women. 

Professor Helen M. Walker has worked out an amusing 
illustration of the folly in assuming there must be cause and 
effect whenever two things vary together. In investigating 
the relationship between age and some physical charac- 
teristics of women, begin by measuring the angle of the feet 
in walking. You will find that the angle tends to be greater 
among older women. You might first consider whether this 
indicates that women grow older because they toe out, and 
you can see immediately that this is ridiculous. So it appears 
that age increases the angle between the feet, and most 
women must come to toe out more as they grow older. 

Any such conclusion is probably false and certainly un- 
warranted. You could only reach it legitimately by studying 
the same women - or possibly equivalent groups - over a 

92 How to Lie with Statistics 

period of time. That would eliminate the factor responsible 
here. Which is that the older women grew up at a time 
when a young lady was taught to toe out in walking, while 
the members of the younger group were learning posture in 
a day when that was discouraged. 

When you find somebody - usually an interested party - 
making a fuss about a correlation, look first of all to see if it 
is not one of this type, produced by the stream of events, the 
trend of the times. In our time it is easy to show a positive 
correlation between any pair of things like these: number of 
students in college, number of inmates in mental insti- 
tutions, consumption of cigarettes, incidence of heart dis- 
ease, use of X-ray machines, production of false teeth, 
salaries of California school teachers, profits of Nevada gam- 
bling halls. To call some one of these the cause of some other 
is manifestly silly. But it is done every day. 

Permitting statistical treatment and the hypnotic pre- 
sence of numbers and decimal points to befog causal re- 
lationships is little better than superstition. And it is often 
more seriously misleading. It is rather like the conviction 
among the people of the New Hebrides that body lice pro- 
duce good health. Observation over the centuries had taught 
them that people in good health usually had lice and sick 
people very often did not. The observation itself was accu- 
rate and sound, as observations made informally over the 
years surprisingly often are. Not so much can be said for the 
conclusion to which these primitive people came from their 
evidence: Lice make a man healthy. Everybody should have 

As we have already noted, scantier evidence than this - 
treated in the statistical mill until common sense could no 
longer penetrate to it - has made many a medical fortune 
and many a medical article in magazines, including pro- 
fessional ones. More sophisticated observers finally got 

Tost Hoc Bides Again 93 

things straightened out in the New Hebrides. As it turned 
out, almost everybody in those circles had lice most of the 
time. It was, you might say, the normal condition of man. 
When, however, anyone took a fever (quite possibly carried 
to him by those same lice) and his body became too hot for 
comfortable habitation, the lice left. There you have cause 
and effect altogether confusingly distorted, reversed, and 



How to 

Misinforming people by the use of statistical material might 
be called statistical manipulation; in a word (though not a 
very good one), statisticulation. 

The title of this book and some of the things in it might 
seem to imply that all such operations are the product of 
intent to deceive. The president of a chapter of the Am- 
erican Statistical Association once called me down for that. 
Not chicanery much of the time, said he, but incompetence. 
There may be something in what he says,* but I am not 

* Author Louis Bromfield is said to have a stock reply to critical 
correspondents when his mail became too heavy for individual 
attention. Without conceding anything and without encouraging 
further correspondence, it still satisfies almost everyone. The key 
sentence: 'There may be something in what you say.' 

How to Statisticulate 95 

certain that one assumption will be less offensive to statisti- 
cians than the other. Possibly more important to keep in mind 
is that the distortion of statistical data and its manipulation 
to an end are not always the work of professional statisti- 
cians. What comes full of virtue from the statistician's 
desk may find itself twisted, exaggerated, over-simplified, 
and distorted-through-selection by salesman, public-relations 
expert, journalist, or advertising copywriter. 

But whoever the guilty party may be in any instance, it is 
hard to grant him the status of blundering innocent. False 
charts in magazines and newspapers frequently sen- 
sationalize by exaggeration, rarely minimize anything. 
Those who present statistical arguments on behalf of indus- 
try are seldom found, in my experience, giving labour or the 
customer a better break than the facts call for, and often 
they give him a worse one. When has a union employed a 
statistical worker so incompetent that he made labour's case 
out weaker than it was? 

As long as the errors remain one-sided, it is not easy to 
attribute them to bungling or accident. 

One of the trickiest ways to misrepresent statistical data is 
by means of a map. A map introduces a fine bag of variables 
in which facts can be concealed and relationships distorted. 
My favourite trophy in this field is The Darkening Shadow'. 
It was distributed not long ago by the First National Bank of 
Boston and reproduced very widely - by so-called taxpayers 
groups, newspapers, and Newsweek magazine. 

It reminds me of the minister who achieved great popularity 
among mothers in his congregation by his flattering comments on 
babies brought in for christening. But when the mothers compared 
notes not one could remember what the man had said, only that it 
had been 'something nice.' Turned out his invariable remark was, 
'My!' (beaming) This is a baby, isn't it!' 

96 How to Lie with Statistics 

The map shows what portion of the American income is 
now being taken, and spent, by the federal government. It 
does this by shading the areas of the states west of the Mis- 
sissippi (excepting only Louisiana, Arkansas, and part of 
Missouri) to indicate that federal spending has become equal 
to the total incomes of the people of those states. 

The deception lies in choosing states having large areas 
but, because of sparse population, relatively small incomes. 
With equal honesty (and equal dishonesty) the map maker 
might have started shading in New York or New England 
and come out with a vastly smaller and less impressive 
shadow. Using the same data he would have produced quite 
a different impression in the mind of anyone who looked at 
his map. No one would have bothered to distribute that one, 
though. At least, I do not know of any powerful group that 
is interested in making public spending appear to be smaller 
than it is. 

If the objective of the map maker had been simply to 
convey information he could haVe done so quite easily. He 
could have chosen a group of in-between states whose total 
area bears the same relation to the area of the country that 
their total income does to the national income. 

The thing that makes this map a particularly flagrant 
effort to misguide is that it is not a new trick of propaganda. 
It is something of a classic, or chestnut. The same bank long 
ago published versions of this map to show federal ex- 
penditures in 1929 and 1937, and these shortly cropped up in 
a standard book, Graphic Presentation, by Willard Cope 
Brinton, as horrible examples. This method 'distorts the 
facts', said Brinton plainly. But the First National goes right 
on drawing its maps, and Newsweek and other people who 
should know better - and possibly do - go right on repro- 
ducing them with neither warning nor apology. 

If you think there's inflation now, consider this. At one 

The darkening shadow (Western style) 

K W «SN.J\ * * j ■■■■,■ \~w 

'"-wj.V^Nr; ■•'! NO. \MINN^ 



W(VM±L neb. V 

To show we won't cheating, we added MD, DEL, end HI. for good measure 

98 How to Lie with Statistics 

time the U.S. Bureau of the Census came up in its annual 
way with word that the 'income of the average family was 
$3,100'. But if you read a newspaper story on 'philanthropic 
giving' handed out by the Russell Sage Foundation you 
learned that, for the same year, it was a notable $5,004. 
Possibly you were pleased to learn that folks were doing so 
well, but you may also have been struck by how poorly that 
figure squared with your own observations. Possibly you 
know the wrong kind of people. 

Now how in the world can Russell Sage and the Bureau of 
the Census be so far apart? The Bureau is talking in medians, 
as of course it should be, but even if the Sage people are 
using a mean the difference should not be quite this great. 
The Russell Sage Foundation, it turns out, discovered this 
remarkable prosperity by producing what can only be de- 
scribed as a phoney family. Their method, they explained 
(when asked for an explanation), was to divide the total 
personal income of the American people by 149,000,000 to 
get an average of $1,251 for each person. 'Which,' they 
added, 'becomes $5,004 in a family of four.' 

This odd piece of statistical manipulation exaggerates in 
two ways. It uses the kind of average called a mean instead 
of the smaller and more informative median . . . something 
we worked over in an earlier chapter. And then it goes on to 
assume that the income of a family is in direct proportion to 
its size. Now I have four children, and I wish things were 
disposed in that way, but they are not. Families of four are 
by no means commonly twice as wealthy as families of 

In fairness to the Russell Sage statisticians, who may be 
presumed innocent of desire to deceive, it should be said that 
they were primarily interested in making a picture of giving 
rather than of getting. The funny figure for family incomes 
was just a by-product. But it spread its deception no less 

How to Statisticulate 99 

effectively for that, and it remains a prime example of why 
little faith can be placed in an unqualified statement of aver- 

For a spurious air of precision that will lend all kinds of 
weight to the most disreputable statistic, consider the deci- 
mal. Ask a hundred citizens how many hours they slept last 

Labour and rest of a peasant woman 


Producing labour 

Other labour 
8h. 2m. 

(3 O 

Rest Sleep 

2h.26m. 5h.43m. 

3 O 


4h. 43m. 

6h. 50m. 

7h. 26m. 

Chart adapted from U.S.S.R. {Scientific Tublishing Institute of 
Victorial Statistics). 

night. Come out with a total of, say, 783-1. Any such data 
are far from precise to begin with. Most people will miss 
their guess by fifteen minutes or more, and there is no as- 
surance that the errors will balance out. We all know some- 
one who will recall five sleepless minutes as half a night of 
tossing insomnia. But go ahead, do your arithmetic, and an- 
nounce that people sleep an average of 7831 hours a night. 
You will sound as if you knew precisely what you were 
talking about. If you had been so foolish as to declare only 
that people sleep 78 (or 'almost 8') hours a night, there 
would have been nothing striking about it. It would have 

ioo How to Lie with Statistics 

sounded like what it was, a poor approximation and no 
more instructive than almost anybody's guess. 

Karl Marx was not above achieving a spurious air of pre- 
cision in the same fashion. In figuring the 'rate of surplus- 
value' in a mill he began with a splendid collection of as- 
sumptions, guesses, and round numbers: 'We assume the 
waste to be 6 per cent . . . the raw material . . . costs in round 
numbers £342. The 10,000 spindles . . . cost, we will assume, 

£1 per spindle The wear and tear we put at 10 per cent. 

. . . The rent of the building we suppose to be £300 ..." He 
says, 'the above data, which may be relied upon, were given 
me by a Manchester spinner.' 

From these approximations Marx calculates that: 'The 
rate of surplus-value is therefore s%2 =153 1J /i3 per cent.' 
For a ten-hour day this gives him 'necessary labour = 3 3 %3 
hours and surplus-labour = 6%3.' 

There's a nice feeling of exactness to that two thirty- 
thirds of an hour, but it's all bluff. 

Percentages offer a fertile field for confusion. And like the 
ever-impressive decimal they can lend an aura of precision 
to the inexact. The United States Department of Labor's 
Monthly Labor Review once stated that of the offers of part- 
time household employment with provisions for car fare, in 
Washington, D.C., during a specified month, 49 per cent 
were at $18 a week. This percentage, it turned out, was 
based on precisely two cases, there having been only forty- 
one offers altogether. Any percentage figure based on a small 
number of cases is likely to be misleading. It is more infor- 
mative to give the figure itself. And when the percentage is 
carried out to decimal places you begin to run the scale from 
the silly to the fraudulent. 

'Buy your Christmast presents now and save 100 per 
cent', advises an advertisement. This sounds like an offer 
worthy of old Santa himself, but it turns out to be merely a 

How to Statisticulate 101 

confusion of base. The reduction is only fifty per cent. The 
saving is one hundred per cent of the reduced or new price, 
it is true, but that isn't what the offer says. 

Likewise when the president of a flower growers' associ- 
ation said, in a newspaper interview, that 'flowers are ioo 
per cent cheaper than four months ago,' he didn't mean that 
florists were now giving them away. But that's what he said. 

In her History of the Standard Oil Company, Ida M. Tar- 
bell went even further. She said that 'price cutting in the 
southwest . . . ranged from 14 to 220 per cent'. That would 
call for seller paying buyer a considerable sum to haul the 
oily stuff away. 

The Columbus Dispatch declared that a manufactured 
product was selling at a profit of 3,800 per cent, basing this 
on a cost of $175 and a selling price of $40. In calculating 
percentage of profits you have a choice of methods (and you 
are obligated to indicate which you are using). If figured on 
cost, this one comes to a profit of 2,185 P er cent; on selling 
price, 95-6 per cent. The Dispatch apparently used a method 
of its own and, as so often seems to happen, got an exagger- 
ated figure to report. 

Even the New York Times lost the Battle of the Shifting 
Base in publishing an Associated Press story from Indi- 

The depression took a stiff wallop on the chin here today. 
Plumbers, plasterers, carpenters, painters and others affiliated 
with the Indianapolis Building Trades Unions were given a 5 per 
cent increase in Wages. That gave back to the men one-fourth of 
the 20 per cent cut they took last winter. 

Sounds reasonable on the face of it - but the decrease has 
been figured on one base - the pay the men were getting in 
the first place - while the increase uses a smaller base, the 
pay level after the cut. 

102 How to Lie with Statistics 

You can check on this bit of statistical misfiguring by 
supposing, for simplicity, that the original wage was $i an 
hour. Cut twenty per cent, it is down to 80 cents. A five per 
cent increase on that is 4 cents, which is not one-fourth but 
one-fifth of the cut. Like so many presumably honest mis- 
takes, this one somehow managed to come out an exagger- 
ation which made a better story. 

All this illustrates why to offset a pay cut of fifty per cent 
you must get a raise of one hundred per cent. 

It was the Times also that once reported that, for a fiscal 
year, air mail 'lost through fire was 4,863 pounds, or a per- 
centage of but 0-00063'. The story said that planes had car- 
ried 7,715,741 pounds of mail during the year. An insurance 
company basing its rates in that way could get into a pack 
of trouble. Figure the loss and you'll find that it came to 
0063 per cent or one hundred times as great as the news- 
paper had it. 

It is the illusion of the shifting base that accounts for the 
trickiness of adding discounts. When a hardware jobber 
offers '50 per cent and 20 per cent off list', he doesn't mean a 
seventy per cent discount. The cut is sixty per cent since the 
twenty per cent is figured on the smaller base left after 
taking off fifty per cent. 

A good deal of bumbling and chicanery have come from 
adding together things that don't add up but merely seem to. 
Children for generations have been using a form of this 
device to prove that they don't go to school. 

You probably recall it. Starting with 365 days to the year 
you can subtract 122 for the one-third of the time you spend 
in bed and another 45 for the three hours a day used in 
eating. From the remaining 198 take away 90 for summer 
vacation and 21 for Christmas and Easter vacations. The 
days that remain are not even enough to provide for Satur- 
days and Sundays. 

How to Statisticulate 103 

Too ancient and obvious a trick to use in serious business, 
you might say. But the United Automobile Workers insist in 
their monthly magazine, Ammunition, that it is still being 
used against them. 

The wide, blue yonder lie also turns up during every strike. 
Every time there is a strike, the Chamber of Commerce adver- 
tises that the strike is costing so many millions of dollars a 

They get the figure by adding up all the cars that would have 
been made if the strikers had worked full time. They add in 
losses to suppliers in the same way. Everything possible is added 
in, including street car fares and the loss to merchants in 

The similar and equally odd notion that percentages can 
be added together as freely as apples has been used against 
authors. See how convincing this one, from The New York 
Times Book Review, sounds. 

The gap between advancing book prices and authors' earn- 
ings, it appears, is due to substantially higher production and 
material costs. Item: plant and manufacturing expenses alone 
have risen as much as 10 to 12 per cent over the last decade, 
materials are up 6 to 9 per cent, selling and advertising expenses 
have climbed upwards of 10 per cent. Combined boosts add up 
to a minimum of 33 per cent (for one company) and to nearly 
40 per cent for some of the smaller houses. 

Actually, if each item making up the cost of publishing 
this book has risen around ten per cent, the total cost must 
have climbed by about that proportion also. The logic that 
permits adding those percentage rises together could lead to 
all sorts of flights of fancy. Buy twenty things today and 
find that each has gone up five per cent over last year. That 
'adds up' to one hundred per cent, and the cost of living has 
doubled. Nonsense. 

104 How to Lie with Statistics 

It's all a little like the tale of the roadside merchant who 
was asked to explain how he could sell rabbit sandwiches so 
cheap. 'Well,' he said, 'I have to put in some horse meat too. 
But I mix 'em fifty-fifty: one horse, one rabbit.' 

A union publication used a cartoon to object to another 
variety of unwarranted adding-up. It showed the boss 
adding one regular hour at $1-50 to one overtime hour at 
$2-25 to one double-time hour at $3 for an average hourly 
wage of $225. It would be hard to find an instance of an 
average with less meaning. 

Another fertile field for being fooled lies in the confusion 
between percentage and percentage points. If your profits 
should climb from three per cent on investment one year to 
six per cent the next, you can make it sound quite modest by 
calling it a rise of three percentage points. With equal vali- 
dity, you can describe it as a one hundred per cent increase. 
For loose handling of this confusing pair watch particularly 
the public-opinion pollers. 

Percentiles are deceptive too. When you are told how 
Johnny stands compared to his classmates in algebra or 
some aptitude, the figure may be a percentile. It means his 
rank in each one hundred students. In a class of three hun- 
dred, for instance, the top three will be at the 99 percentile, 
the next three at the 98, and so on. The odd thing about per- 
centiles is that a student with a 99-percentile rating is prob- 
ably quite a bit superior to one standing at 90, while those at 
the 40 and 60 percentiles may be of nearly equal achieve- 
ment. This comes from the habit that so many charac- 
teristics have of clustering about their own average, forming 
the 'normal' bell curve we mentioned in an early chapter. 

Occasionally a battle of the statisticians develops, and 
even the most unsophisticated observer cannot fail to smell 
a rat. Honest men get a break when statisticulators fall out. 
The Steel Industry Board has pointed out some of the 

How to Statisticulate 105 

monkey business in which both steel companies and unions 
have indulged. To show how good business had been in the 
year just ended (as evidence that the companies could well 
afford a raise), the union compared that year's productivity 
with the productivity of 1939- a year of especially low 
volume. The companies, not to be outdone in the deception 
derby, insisted on making their comparisons on a basis of 
money received by the employees rather than average 
hourly earnings. The point to this was that so many workers 
had been on part time in the earlier year that their incomes 
were bound to have grown even if wage rates had not risen 
at all. 

Time magazine, notable for the consistent excellence of 
its graphics, published a chart that is an amusing example of 
how statistics can pull out of the bag almost anything that 
may be wanted. Faced with a choice of methods, equally 
valid, one favouring the management viewpoint and the 
other favouring labour, Time simply used both. The chart 
was really two charts, one superimposed upon the other. 
They used the same data. 

One showed wages and profits in billions of dollars. It was 
evident that although both were rising, the increase in wages 
in the last year was roughly twice that in profits. And that 
wages involved perhaps six times as many dollars as profits 
did. The great inflationary pressure, it appeared, came from 

The other part of the dual chart expressed the changes as 
percentages of increase. The wage line was relatively flat. 
The profit line shot sharply upwards. Profits, it might be 
inferred, were principally responsible for inflation. 

You could take your choice of conclusions. Or, perhaps 
better, you could easily see that neither element could 
properly be singled out as the guilty one. It is sometimes a 
substantial service simply to point out that a subject in 

Time chart 

Redrawn with the kind permission of Time magazine as an 
example of a non-lying chart. 

How to Statisticulate 107 

controversy is not as open-and-shut as it has been made to 

Index numbers are vital matters to millions of people now 
that wage rates are often tied to them. It is perhaps worth 
noting what can be done to make them dance to any man's 

To take the simplest possible example, let's say that milk 
cost 1 op a quart last year and bread was iop a loaf. This 
year milk is down to 5p and bread is up to 2op. Now what 






rices u 




Last year 

This year 

would you like to prove? Cost of living up? Cost of living 
down? Or no change? 

Consider last year as the base period, making the prices of 
that time 100 per cent. Since the price of milk has since 
dropped to half (50 per cent) and the price of bread has 
doubled (200 per cent) and the average of 50 and 200 is 125, 
prices have gone up 25 per cent. 

Try it again, taking this year as base period. Milk used to 
cost 200 per cent as much as it does now and bread was 

108 How to Lie with Statistics 

selling for 50 per cent as much. Average: 125 per cent. 
Prices used to be 25 per cent higher than they are now. 

To prove that the cost level hasn't changed at all we 
simply switch to the geometric average and use either 
period as the base. This is a little different from the arith- 
metic average, or mean, that we have been using but it is a 
perfectly legitimate kind of figure and in some cases the 










Last year 

This year 

most useful and revealing. To get the geometric average of 
three numbers you multiply them together and derive the 
cube root. For four items, the fourth root; for two, the 
square root. Like that. 

Take last year as the base and call its price level 100. 
Actually you multiply the 100 per cent for each item 
together and take the root, which is 100. For this year, milk 
being at 50 per cent of last year and bread at 200 per cent, 
multiply 50 by 200 to get 10,000. The square root, which is 
the geometric average, is 100. Prices have not gone up or 

How to Statisticulate 109 

The fact is that, despite its mathematical base, statistics is 
as much an art as it is a science. A great many manipulations 
and even distortions are possible within the bounds of pro- 
priety. Often the statistician must choose among methods, a 
subjective process, and find the one that he will use to re- 
present the facts. In commercial practice he is about as un- 
likely to select an unfavourable method as a copywriter is to 
call his sponsor's product flimsy and cheap when he might 
as well say light and economical. 

Even the man in academic work may have a bias (possibly 
unconscious) to favour, a point to prove, an axe to grind. 

This suggests giving statistical material, the facts and 
figures in newspapers and books, magazines and advertising, 
a very sharp second look before accepting any of them. 
Sometimes a careful squint will sharpen the focus. But arbi- 
trarily rejecting statistical methods makes no sense either. 
That is like refusing to read because writers sometimes use 
words to hide facts and relationships rather than to reveal 
them. After all, a political candidate in Florida not long ago 
made considerable capital by accusing his opponent of 
'practising celibacy'. A New York exhibitor of the motion 
picture Quo Vadis used huge type to quote the New York 
Times as calling it 'historical pretentiousness'. And the 
makers of Crazy Water Crystals, a proprietary medicine, 
have been advertising their product as providing 'quick, 
ephemeral relief. 




How to * 

Talk Back to a 


So far, I have been addressing you rather as if you were a 
pirate with a yen for instruction in the finer points of cutlass 
work. In this concluding chapter I'll drop that literary 
device. I'll face up to the serious purpose that I like to think 
lurks just beneath the surface of this book: explaining how 
to look a phoney statistic in the eye and face it down; and 
no less important, how to recognize sound and usable data in 
that wilderness of fraud to which the previous chapters 
have been largely devoted. 

Not all the statistical information that you may come 
upon can be tested with the sureness of chemical analysis 
or of what goes on in an assayer's laboratory. But you 
can prod the stuff with five simple questions, and by find- 
ing the answers avoid learning a remarkable lot that 
isn't so. 

How to Talk Back to a Statistic in 

Who Says So? 

About the first thing to look for is bias - the laboratory with 
something to prove for the sake of a theory, a reputation, or 
a fee; the newspaper whose aim is a good story; labour or 
management with a wage level at stake. 

Look for conscious bias. The method may be direct mis- 
statement or it may be ambiguous statement that serves as 
well and cannot be convicted. It may be selection of favour- 
able data and suppression of unfavourable. Units of 
measurement may be shifted, as with the practice of using 
one year for one comparison and sliding over to a more 
favourable year for another. An improper measure may be 
used: a mean where a median would be more informative 
(perhaps all too informative), with the trickery covered by 
the unqualified word 'average'. 

Look sharply for unconscious bias. It is often more 
dangerous. In the charts and predictions of many stat- 
isticians and economists in 1928 it operated to produce re- 
markable things. The cracks in the economic structure were 
joyously overlooked, and all sorts of evidence were adduced 
and statistically supported to show that we had no more 
than entered the stream of prosperity. 

It may take at least a second look to find out who-says-so. 
The who may be hidden by what Stephen Potter, the Life- 
manship man, would probably call the 'O.K. name'. Any- 
thing smacking of the medical profession is an O.K. name. 
Scientific laboratories have O.K. names. So do universities, 
more especially ones eminent in technical work. The 
writer who proved a few chapters back that higher educa- 
tion jeopardizes a girl's chance to marry made good use of 
the O.K. name of Cornell. Please note that while the data 
came from Cornell, the conclusions were entirely the 

H2 How to Lie with Statistics 

writer's own. But the O.K. name helps you carry away a 
misimpression of 'Cornell University says . . .' 

When an O.K. name is cited, make sure that the authority 
stands behind the information, not merely somewhere 
alongside it. 

You may have read a proud announcement by the Chi- 
cago Journal ol Commerce. That publication had made a 
survey. Of 169 corporations that replied to a poll on price 
gouging and hoarding, two-thirds declared that they were 
absorbing price increases produced by the police action, or 
undeclared war, in which the United States was then as 
usual engaged in the Far East. 'The survey shows,' said the 
Journal (look sharp whenever you meet those words!), 'that 
corporations have done exactly the opposite of what the 
enemies of the American business system have charged.' 
This is an obvious place to ask, 'Who says so?' since the 
Journal of Commerce might be regarded as an interested 
party. It is also a splendid place to ask our second test ques- 

How Does He Know? 

It turns out that the Journal had begun by sending its ques- 
tionnaires to 1,200 large companies. Only fourteen per cent 
had replied. Eighty-six per cent had not cared to say any- 
thing in public on whether they were hoarding or price 

The Journal had put a remarkably good face on things, 
but the fact remains that there was little to brag about. It 
came down to this: Of 1,200 companies polled, nine per cent 
said they had not raised prices, five per cent said they had, 
and eighty-six per cent wouldn't say. Those that had replied 
constituted a sample in which bias might be suspected. 

How to Talk Back to a Statistic 113 

Watch out for evidence of a biased sample, one that has 
been selected improperly or - as with this one - has selected 
itself. Ask the question we dealt with in an early chapter: Is 
the sample large enough to permit any reliable con- 

Similarly with a reported correlation: Is it big enough to 
mean anything? Are there enough cases to add up to any 
significance? You cannot, as a casual reader, apply tests of 
significance or come to exact conclusions as to the adequacy 
of a sample. On a good many of the things you see reported, 
however, you will be able to tell at a glance - a good long 
glance, perhaps -that there just weren't enough cases to 
convince any reasoning person of anything. 

What's Missing? 

You won't always be told how many cases. The absence of 
such a figure, particularly when the source is an interested 
one, is enough to throw suspicion on the whole thing. Simi- 
larly a correlation given without a measure of reliability 
(probable error, standard error) is not to be taken very 

Watch out for an average, variety unspecified, in any 
matter where mean and median might be expected to differ 

Many figures lose meaning because a comparison is miss- 
ing. An article in Look magazine says, in connection with 
Mongolism, that 'one study shows that in 2,800 cases, over 
half of the mothers were 35 or over'. Getting any meaning 
from this depends upon your knowing something about the 
ages at which women in general produce babies. Few of us 
know things like that. 

ii4 How to Lie with Statistics 

Here is a pollution note from nearly a generation ago, 
from a New Yorker magazine 'Letter from London': 

The Ministry of Health's recently published figures showing 
that in the week of the great fog the death rate for Greater 
London jumped by twenty-eight hundred were a shock to the 
public, which is used to regarding Britain's unpleasant climatic 
effects as nuisances rather than as killers . . . The extraordinary 
lethal properties of this winter's prize visitation . . . 

But how lethal was the visitation? Was it exceptional for 
the death rate to be that much higher than usual in a week? 
All such things do vary. And what about ensuing weeks? Did 
the death rate drop below average, indicating that if the 
fog killed people they were largely those who would have 
died shortly anyway? The figure sounds impressive, but 
the absence of other figures takes away most of its mean- 

Sometimes it is percentages that are given and raw figures 
that are missing, and this can be deceptive too. Long ago, 
when Johns Hopkins University had just begun to admit 
women students, someone not particularly enamoured of 
co-education reported a real shocker: Thirty-three and one- 
third per cent of the women at Hopkins had married faculty 
members! The raw figures gave a clearer picture. There were 
three women enrolled at the time, and one of them had 
married a faculty man. 

Some years ago the Boston Chamber of Commerce chose 
its American Women of Achievement. Of the sixteen among 
them who were also in Who's Who, it was announced that 
they had 'sixty academic degrees and eighteen children'. 
That sounds like an informative picture of the group until 
you discover that among the women were Dean Virginia 
Gildersleeve and Mrs Lillian M. Gilbreth. Those two had a 
full third of the degrees between them. And Mrs Gilbreth, 

How to Talk Back to a Statistic 1 15 

about whose offspring Cheaper by the Dozen was written, 
supplied two-thirds of the children. 

A corporation was able to announce that its stock was 
held by 3,003 persons, who had an average of 660 shares 
each. This was true. It was also true that of the two million 
shares of stock in the corporation three men held three-quar- 
ters and three thousand persons held the other one-fourth 
among them. 

If you are handed an index, you may ask what's missing 
there. It may be the base, a base chosen to give a distorted 
picture. A national labour organization once showed that 
indexes of profits and production had risen much more 
rapidly after the depression than an index of wages had. As 
an argument for wage increases this demonstration lost its 
potency when someone dug out the missing figures. It could 
be seen then that profits had been almost bound to rise more 
rapidly in percentage than wages simply because profits had 
reached a lower point, giving a smaller base. 

Sometimes what is missing is the factor that caused a 
change to occur. This omission leaves the implication that 
some other, more desired, factor is responsible. Figures pub- 
lished one year attempted to show that business was on the 
upgrade by pointing out that April retail sales were greater 
than in the year before. What was missing was the fact that 
Easter had come in March in the earlier year and in April in 
the later year. 

A report of a great increase in deaths from cancer in the 
last quarter-century is misleading unless you know how 
much of it is a product of such extraneous factors as these: 
Cancer is often listed now where 'causes unknown' was 
formerly used; autopsies are more frequent, giving surer 
diagnoses; reporting and compiling of medical statistics are 
more complete; and people more frequently reach the most 
susceptible ages now. And if you are looking at total deaths 

1 1 6 How to Lie with Statistics 

rather than the death rate, don't neglect the fact that there 
are more people now than there used to be. 

Did Somebody Change the Subject? 

When assaying a statistic, watch out for a switch some- 
where between the raw figure and the conclusion. One thing 
is all too often reported as another. 

As just indicated, more reported cases of a disease are not 
always the same thing as more cases of the disease. A straw- 
vote victory for a candidate is not always negotiable at the 
polls. An expressed preference by a 'cross-section' of a maga- 
zine's readers for articles on world affairs is no final proof 
that they would read the articles if they were published. 

A year came when encephalitis cases reported in the cen- 
tral valley of California were triple the figure for the worst 
previous year. Many alarmed residents shipped their chil- 
dren away. But when the reckoning was in, there had been 
no great increase in deaths from sleeping sickness. What had 
happened was that state and federal health people had come 
in in great numbers to tackle a long-time problem; as a result 
of their efforts a great many low-grade cases were recorded 
that in other years would have been overlooked, possibly 
not even recognized. 

It is all reminiscent of the way that Lincoln Steffens and 
Jacob A. Riis, as New York newspapermen, once created a 
crime wave. Crime cases in the papers reached such pro- 
portions, both in numbers and in space and big type given to 
them, that the public demanded action. Theodore Roosevelt, 
as president of the reform Police Board, was seriously em- 
barrassed. He put an end to the crime wave simply by asking 
Steffens and Riis to lay off. It had all come about simply 
because the reporters, led by those two, had got into com- 

How to Talk Back to a Statistic 117 

petition as to who could dig up the most burglaries and 
whatnot. The official police record showed no increase at all. 

'The British male over £ years of age soaks himself in a hot 
tub on an average of 17 times a week in the winter and 2-i 
times in the summer,' says a newspaper story. 'British 
women average 1 5 baths a week in the winter and 2-0 in the 
summer.' The source is a Ministry of Works hot-water 
survey of '6,ooo representative British homes'. The sample 
was representative, it says, and seems quite adequate in size 
to justify the conclusion in the San Francisco Chronicle's 
amusing headline: British he's bathe more than 

The figures would be more informative if there were some 
indication of whether they are means or medians. However, 
the major weakness is that the subject has been changed. 
What the Ministry really found out is how often these 
people said they bathed, not how often they did so. When a 
subject is as intimate as this one is, with the British bath- 
taking tradition involved, saying and doing may not be the 
same thing at all. British he's may or may not bathe oftener 
than she's; all that can safely be concluded is that they say 
they do. 

Here are some more varieties of change-of-subject to 
watch out for. 

A back-to-the-farm movement was discerned when a 
census showed half a million more farms in the U.S. than 
five years earlier. But the two counts were not talking about 
the same thing. The definition of farm used by the Bureau of 
the Census had been changed; it took in at least 300,000 
farms that would not have been so listed under the earlier 

Strange things crop up when figures are based on what 
people say - even about things that seem to be objective 
facts. Census reports have shown more people at thirty-five 

1 1 8 How to Lie with Statistics 

years of age, for instance, than at either thirty-four or thirty- 
six. The false picture comes from one family member's re- 
porting the ages of the others and, not being sure of the 
exact ages, tending to round them off to a familiar multiple 
of five. One way to get around this: ask for birth dates in- 

The 'population' of a large area in China was 28 million. 
Five years later it was 105 million. Very little of that in- 
crease was real; the great difference could be explained 
only by taking into account the purposes of the two enu- 
merations and the way people would be inclined to feel 
about being counted in each instance. The first census was 
for tax and military purposes, the second for famine relief. 

Something of the same sort has happened in the United 
States. A decennial census found more people in the sixty- 
five-to-seventy age group than there were in the fifty-five- 
to-sixty group ten years before. The difference could not be 
accounted for by immigration. Most of it could be a product 
of large-scale falsifying of ages by people eager to collect 
social security. Also possible is that some of the earlier ages 
were understated out of vanity. 

Another kind of change-of-subject is represented by U.S. 
Senator William Langer's cry, back in days when San Fran- 
cisco's notorious island was a boarding house for hard cases 
and hotels charged less than they do now, that 'we could 
take a prisoner from Alcatraz and board him at the Wal- 
dorf-Astoria cheaper . . .' The North Dakotan was referring 
to earlier statements that it cost eight dollars a day to main- 
tain a prisoner at Alcatraz, 'the cost of a room at a good San 
Francisco hotel'. The subject has been changed from total 
maintenance cost (Alcatraz) to hotel-room rent alone. 

The post hoc variety of pretentious nonsense is another 
way of changing the subject without seeming to. The change 
of something with something else is presented as because of. 

How to Talk Back to a Statistic 119 

The magazine Electrical World once offered a composite 
chart in an editiorial on 'What Electricity Means to Am- 
erica'. You could see from it that as 'electrical horsepower in 
factories' climbed, so did 'average wages per hour'. At the 
same time 'average hours per week' dropped. All these 
things are long-time trends, of course, and there is no evi- 
dence at all that any one of them has produced any other. 

And then there are the firsters. Almost anybody can claim 
to be first in something if he is not too particular what it is. 
At the end of 1952 two New York newspapers were each 
insisting on first rank in grocery advertising. Both were right 
too, in a way. The World-Telegram went on to explain that 
it was first in full-run advertising, the kind that appears in all 
copies, which is the only kind it runs. The Journal- American 
insisted that total linage was what counted and that it was 
first in that. This is the kind of reaching for a superlative 
that leads the weather reporter on the radio to label a quite 
normal day 'the hottest June second since 1967'. 

Change-of-subject makes it difficult to compare cost when 
you contemplate borrowing money either directly or in the 
form of instalment buying. Six per cent sounds like six per 
cent - but it may not be at all. 

If you borrow £100 from a bank at six per cent interest 
and pay it back in equal monthly instalments for a year, the 
price you pay for the use of the money is about £3. But 
another six per cent loan, on the basis sometimes called £6 
on the £100, will cost you twice as much. That's the way 
most automobile loans are figured. It is very tricky. 

The point is that you don't have the £100 for a year. By 
the end of six months you have paid back half of it. If you 
are charged at £6 on the £roo, or six per cent of the amount, 
you really pay interest at nearly twelve per cent. 

Even worse was what happened to some careless pur- 
chasers of freezer-food plans in America. They were quoted 

1 20 How to Lie with Statistics 

a figure of anywhere from six to twelve per cent. It sounded 
like interest, but it was not. It was an on-the-dollar figure 
and, worst of all, the time was often six months rather than 
a year. Now £12 on the £100 for money to be paid back 
regularly over half a year works out to something like forty- 
eight per cent real interest. It is no wonder that so many 
customers defaulted and so many food plans blew up. 

Sometimes the semantic approach will be used to change 
the subject. Here is an item from Business Week maga- 

Accountants have decided that 'surplus' is a nasty word. They 
propose eliminating it from corporate balance sheets. The Com- 
mittee on Accounting Procedure of the American Institute of 
Accountants says: . . . Use such descriptive terms as 'retained 
earnings' or 'appreciation of fixed assets'. 

This one is from a newspaper story reporting Standard 
Oil's record-breaking revenue and net profit of a million 
dollars a day. 

Possibly the directors may be thinking some time of splitting 
the stock for there may be an advantage ... if the profits per 
share do not look so large 

Does It Make Sense? 

'Does it make sense?' will often cut a statistic down to size 
when the whole rigmarole is based on an unproved as- 
sumption. You may be familiar with the Rudolf Flesch 
readability formula. It purports to measure how easy a piece 
of prose is to read, by such simple and objective items as 
length of words and sentences. Like all devices for reducing 
the imponderable to a number and substituting arithmetic 
for judgement, it is an appealing idea. At least it has 

How to Talk Back to a Statistic 1 2 1 

appealed to people who employ writers, such as newspaper 
publishers, even if not to many writers themselves. The as- 
sumption in the formula is that such things as word length 
determine readability. This, to be ornery about it, remains to 
be proved. 

A man named Robert A. Dufour put the Flesch formula to 
trial on some literature that he found handy. It showed 'The 
Legend of Sleepy Hollow' to be half again as hard to read as 
Plato's Republic. The Sinclair Lewis novel Cass Timberlane 
was rated more difficult than an essay by Jacques Maritain, 
'The Spiritual Value of Art'. A likely story. 

Many a statistic is false on its face. It gets by only because 
the magic of numbers brings about a suspension of common 
sense. Leonard Engel, in a Harper's article, has listed a few of 
the medical variety. 

An example is the calculation of a well-known urologist that 
there are eight million cases of cancer of the prostate gland in 
the United States - which would be enough to provide i-i car- 
cinomatous prostate glands for every male in the susceptible 
age group! Another is a prominent neurologist's estimate that 
one American in twelve suffers from migraine; since migraine is 
responsible for a third of chronic headache cases, this would 
mean that a quarter of us must suffer from disabling headaches. 
Still another is the figure of 250,000 often given for the number 
of multiple sclerosis cases; death data indicate that there can be, 
happily, no more than thirty to forty thousand cases of this 
paralytic disease in the country. 

Hearings on amendments to the Social Security Act have 
been haunted by various forms of a statement that makes 
sense only when not looked at closely. It is an argument that 
goes like this: Since life expectancy is only about sixty-three 
years, it is a sham and a fraud to set up a social-security plan 
with a retirement age of sixty-five, because virtually every- 
body dies before that. 

122 How to Lie with Statistics 

You can rebut that one by looking around at people you 
know. The basic fallacy, however, is that the figure refers to 
expectancy at birth, and so about half the babies born can 
expect to live longer than that. The figure, incidentally, 
came from the 1939-41 period and remained in use long 
after it was out of date. Presumably the current figure, cal- 
culated a generation later, of 697 will produce a new and 
equally silly argument to the effect that practically every- 
body now lives to be sixty-five. 

Product planning at a big electrical-appliance company 
was going great guns some years ago on the basis of a de- 
clining birth rate, something that had been taken for granted 
for a long time. Plans called for emphasis on small-capacity 
appliances, apartment-size refrigerators. Then one of the 
planners had an attack of common sense: He came out of his 
graphs and charts long enough to notice that he and his co- 
workers and his friends and his neighbours and his former 
classmates with few exceptions either had three or four chil- 
dren or planned to. This led to some open-minded inves- 
tigating and charting - and the company shortly turned its 
emphasis most profitably to big-family models. It is to be 
hoped that the planners will respond more quickly to the 
present turnaround. 

The impressively precise figure is something else that con- 
tradicts common sense. A study reported in New York City 
newspapers announced that a working woman living with 
her family needed a weekly pay cheque of $40- 13 for 
adequate support. Anyone who has not suspended all logical 
processes while reading his paper will realize that the cost of 
keeping body and soul together cannot be calculated to the 
last cent. But there is a dreadful temptation; '$40- 13' sounds 
so much more knowing than 'about $40'. 

You are entitled to look with the same suspicion on the 
report, some years ago, by the American Petroleum Indus- 

How to Talk Back to a Statistic 123 

tries Committee that the average yearly tax bill for auto- 
mobiles is $51-13. 

Extrapolations are useful, particularly in that form of 
soothsaying called forecasting trends. But in looking at the 
figures or the charts made from them, it is necessary to re- 
member one thing constantly: The trend-to-now may be a 
fact, but the future trend represents no more than an edu- 
cated guess. Implicit in it is 'everything else being equal' and 
'present trends continuing'. And somehow everything else 
refuses to remain equal, else life would be dull indeed. 

For a sample of the nonsense inherent in uncontrolled 
extrapolation, consider the trend of television. The number 
of sets in American homes increased around 10,000 per cent 
in one five-year period early in the game. Project this for the 
next five years and you'd have found that there were about 
to be a couple of thousand million of the things. Heaven 
forfend, or forty sets to the family. If you want to be sillier 
yet, begin with a base year even earlier in the telly scheme 
of things and you can just as well 'prove' that each family 
will soon have not forty but forty thousand sets. 

What Harry Truman did to Tom Dewey, in a U.S. Presi- 
dential-election upset unparalleled before or since, is 
nothing to what Truman did to the poll people. A Govern- 
ment research man, Morris Hansen, has called that Gallup 
election forecast 'the most publicized statistical error in 
human history'. 

It was a paragon of accuracy, however, compared to 
some of our most widely used estimates of future popu- 
lation, which have earned a nationwide horselaugh. As late 
as 1938 a Presidential commission loaded with experts 
doubted that the population of the United States would ever 
reach 140 million; it was 12 million more than that just 
twelve years later. Yet college textbooks published so re- 
cently that they were still in use at that time predicted a 

1 24 How to Lie with Statistics 

peak population of not more than 150 million and figured it 
would take until about 1980 to reach it. These fearful under- 
estimates came from assuming that a trend would continue 
without change. A similar assumption a century ago did as 
badly in the opposite direction because it assumed con- 
tinuation of population-increase rate of 1790 to i860. In his 
second message to Congress, Abraham Lincoln predicted the 
ILS. population would reach 251,689,914 in 1930. 

Not long after that, in 1874, Mark Twain summed up 
the nonsense side of extrapolation in Life on the Mis- 

In the space of one hundred and seventy-six years the Lower 
Mississippi has shortened itself two hundred and forty-two 
miles. That is an average of a trifle over one mile and a third per 
year. Therefore, any calm person, who is not blind or idiotic, 
can see that in the Old Oolitic Silurian period, just a million 
years ago next November, the Lower Mississippi River was 
upward of one million three hundred thousand miles long, and 
stuck out over the Gulf of Mexico like a fishing-rod. And by the 
same token any person can see that seven hundred and forty- 
two years from now the Lower Mississippi will be only a mile 
and three-quarters long, and Cairo and New Orleans will have 
joined their streets together, and be plodding comfortably along 
under a single mayor and a mutual board of aldermen. There is 
something fascinating about science. One gets such wholesale 
returns of conjecture out of such a trifling investment of fact. 


The Panda's Thumb Stephen Jay Gou Id 

More reflections on natural history from the author of Ever Since Darwin. 
'A quirky and provocative exploration of the nature of evolution ... 
wonderfully entertaining' - Sunday Telegraph 

Godel, Escher, Bach: An Eternal Golden Braid Douglas F. Hofstadter 

'Every few decades an unknown author brings out a book of such depth, 
clarity, range, wit, beauty and originality that it is recognized at once as a 
major literary event' - Martin Gardner. 'Leaves you feeling you have had 
a first-class workout in the best mental gymnasium in town' - New 

The Double Helix James D. Watson 

Watson's vivid and outspoken account of how he and Crick discovered the 
structure of DNA (and won themselves a Nobel Prize) - one of the 
greatest scientific achievements of the century. 

The Quantum World J. C. Polkinghorne 

Quantum mechanics has revolutionized our views about the structure of 
the physical world - yet after more than fifty years it remains controver- 
sial. This 'delightful book' (The Times Educational Supplement) succeeds 
superbly in rendering an important and complex debate both clear and 

Einstein's Universe Nigel Calder 

'A valuable contribution to the demystification of relativity' - Nature 

Mathematical Circus Martin Gardner 

A mind-bending collection of puzzles and paradoxes, games and 
diversions from the undisputed master of recreational mathematics. 




QED Richard Feynman 

The Strange Theory of Light and Matter 

Quantum thermodynamics - or QED for short - is the 'strange theory' 

- that explains how light and electrons interact. 'Physics Nobelist Feyn- 
man simply cannot help being original. In this quirky, fascinating book, he 
explains to laymen the quantum theory of light - a theory to which he 
made decisive contributions' - New Yorker 

God and the New Physics Paul Davies 

Can science, now come of age, offer a surer path to God than religion? 
This 'very interesting' (New Scientist) book suggests it can. 

Does God Play Dice? Ian Stewart 
The New Mathematics of Chaos 

To cope with the truth of a chaotic world, pioneering mathematicians have 
developed chaos theory. Does God Play Dice? makes accessible the basic 
principles and many practical applications of one of the most extraordi- 
nary - and mindbending - breakthroughs in recent years. 'Engaging, 
accurate and accessible to the uninitiated' - Nature 

The Blind Watchmaker Richard Dawkins 

'An enchantingly witty and persuasive neo-Darwinist attack on the anti- 
evolutionists, pleasurably intelligible to the scientifically illiterate' 

- Hermione Lee in the Observer Books of the Year 

The Making of the Atomic Bomb Richard Rhodes 

'Rhodes handles his rich trove of material with the skill of a master 
novelist ... his portraits of the leading figures are three-dimensional and 
penetrating ... the sheer momentum of the narrative is breathtaking ... a 
book to read and to read again' - Walter C. Patterson in the Guardian 

Asimov's New Guide to Science Isaac Asimov 

A classic work brought up to date - far and away the best one-volume 
survey of all the physical and biological sciences. 


In every corner of the world, on every subject under the sun. Penguin 
represents quality and variety - the very best in publishing today. 

For complete information about books available from Penguin - including 
Puffins , Penguin Classics and Arkana - and how to order them , write to us 
at the appropriate address below. Please note that for copyright reasons 
the selection of books varies from country to country. 

In the United Kingdom: Please write to Dept E.P.. Penguin Books Ltd, 
Harmondsworth, Middlesex, UB70DA. 

If you have any difficulty in obtaining a title , please send your order with the correct 
money, plus ten percent for postage and packaging, to PO Box Noll, West Drayton, 

In the United States: Please write to Depl BA, Penguin, 299 Murray Hill Parkway, 
East Rutherford, New Jersey 07073 

in Canada: Please write to Penguin Books Canada Ltd, 2801 John Street, Markham, 
Ontario L3R 1B4 

In Australia: Please write to the Marketing Department, Penguin Books Australia 
Ltd, P.O. Box 257, Ringwood, Victoria 3134 

In New Zealand: Please write to the Marketing Department. Penguin Books (NZ) 
Ltd, Private Bag, Takapuna, Auckland 9 

In India: Please write to Penguin Overseas Ltd, 706 Eros Apartments, 
56 Nehru Place, New Delhi, 110019 

In the Netherlands: Please write to Penguin Books Netherlands B. V., Postbus 195, 
NL-1380AD Weesp 

In West Germany: Please write to Penguin Books Ltd, Friedrichstrasse 10-12, 
D-6000 Frankfurt I Main I 

In Spain: Please write to Alhambra Longman S.A., Fernandez de la Hoz 9, E-28010 

In Italy: Please write to Penguin Italia s.r.l.. Via Como4, 1-20096 Pioltello (Milano) 

In France: Please write to Penguin Books Ltd, 39 Rue de Montmorency, 
F-75003 Paris 

In Japan: Please write to Longman Penguin Japan Co Ltd, Yamaguchi Building, 
2-12-9 Kanda Jimbocho, Chiyoda-Ku, Tokyo 101 

Penguin Mathematics 

'Round numbers,' pronounced Dr Johnson, 'are 
always false.' 

But not, of course, the precise and scientific 

calculations of trained statisticians with their 

decimals and percentages. The computer, like the 

camera, cannot lie. Not without help anyhow. 

Describing his book as "a sort of primer in ways 
to use statistics to deceive', Darrefl Huff goes on 

to introduce the beginner to the niceties of 
samples (random or stratified random), averages 

(mean, median or modal), errors (probable, 

standard or unintentional), graphs, indexes and 

other tools of democratic persuasion. 

When it was first published this now classic 

book was hailed as a splendid piece of 

blasphemy against the preposterous religion of 

our time'. Today statistics continue to baffle us, 

and this trenchant book remains an invaluable 

guide through the maze of facts and figures that 

is designed to make us believe anything, 

COvor design try Mel Caiman and Phil: p ThfMfipjOrt 






ISBN Q-14-D1 3629-0